
UNI 



* 



THE 



PRACTICAL APPLICATION 



Jflt 



OF THE 



Slide Valve and Link Motion 



TO 



STATIONARY, PORTABLE,- LOCOMOTIVE, AND 
MARINE ENGINES, 



NEW AIS T D SIMPLE METHODS 



PROPORTIONING THE PARTS. 



BY 

WILLIAM S. AUCHINCLOSS, C. E., 

H 
MEM. AMEIi. SOC. CIV. ENG. 



THIRT3 EDITION, 
REVISED AND ENLARGED. 



NEW YORK: 
D. VAN NOSTRAND, PUBLISHER, 

23 MURRAY, AND 27 WARREN STS. 

TsToT 






K^S'V 



Entered, according to Act of Congress, in the year 1870, by 

WILLIAM S. AUCHINCLOSS, 

In the Clerk's Office of the District Court of the United States for the Southern District of 

New York. 




«*%* 



Electrotyped by Smith &, McDougal, S2 & 84 ge 






inn Street 



PREFACE. 



The main object of this Treatise on the Link and Slide Valve, 
is to place in the hands of the Mechanical Engineer and Draughts- 
man, a simple method for determining the proportions suitable to 
any Link Motion, without the assistance of an expensive and cum- 
brous model, or the delays incident to its manipulation. 

Secondarily, to supply the Student of Steam Engineering with 
a comprehensive view of those causes which regulate both the 
form and dimension of the cylinder, slide valve and eccentric. 
This portion of the work has grown incidentally out of the first ; 
for as the link merely combines the action of the two eccentrics, it 
was obviously necessary that the functions of one of these should 
be clearly understood before an attempt was made to develop 
the laws of their joint action. It is hoped, however, that these 
Parts I. and II. will not prove entirely devoid of interest to the 
skilled designer, but that they will at least receive a hasty survey, 
for the sake of the light they throw on the general subject through 
the medium of Part III. 

We are aware, that most Engineers consider the use of a model 
as absolutely indispensable to the proper adjustment of a Link 
Motion, and that they are wont to look with skepticism upon all 
efforts made to solve the problem by other means. So far as these 
feelings are entertained against an algebraic or trigonometric 
solution they rest on a firm foundation and receive our hearty 
approval ; for we have been led to believe from careful investigation 
that it is utterly impossible to construct for this case a formula of 
any practical value, since the question involves from sixteen to 



IV PEEFACE. 

twenty variable quantities, the majority of which exert a controlling 
influence on the motion and many introduce irregularities quite 
beyond the powers of algebraic expression. 

But at the very point where such analysis fails, geometric con- 
struction tenders its most efficient aid and furnishes a simple 
solution of this abstruse problem. The method of investigation has 
been copiously illustrated with cuts — Part IV — showing the link 
template drawn in all of its important positions. These have been 
considered of greater importance for a clear understanding of the 
subject than the employment of a more diffuse explanation. They 
are however apt to produce at first sight an erroneous impression 
regarding the conciseness of the method, but this will always be 
corrected by a single construction trial, which at once reveals how 
small an amount of work is actually required for accomplishing the 
object in view. 

The Table of crank angles for different locations of the piston 
cannot fail to effect a great saving of time, for it enables the 
designer to instantly locate the eccentrics for any piston position, 
without resort to laborious construction. 

Besides treating of the various methods by which a link should 
be suspended for accomplishing certain results, the manner of 
attaching the eccentric rods has been carefully examined and 
diagrams presented that show what form should be adopted for 
meeting most directly the requirements of an accurate adjustment. 

A brief discussion of the subject of independent cut-offs will be 
found in Part V., together with general remarks on Friction, Clear- 
ance, Travel, &c. 

We have added an Appendix for the benefit of those who desire 
a mathematical investigation of the subject of crank and piston 
motion and who would fain inquire more minutely into the princi- 
ples involved in the Stkoke Table. This has purposely been 
separated from the body of the work, w T hich we have aimed as far 
as possible to preserve free from all algebraic formulEe, in order to 
render it more acceptable to the majority of mechanics. 

We trust that these will appreciate the peculiar directness of the 



PREFACE. v 

solutions effected by the Travel Scale, in that it determines im- 
mediately the very dimensions desired, without taxing the investi- 
gator's patience by leading him through intricate constructions to 
an uncertain result. 

The work is now presented to the Engineering community, 
not without consciousness of its imperfections, yet with the hope 
that it will tend to simplify in many minds the subject of eccentric 
and link motion and serve as a stepping-stone to further discoveries: 

W. S. A. 
New York. March, 1869. 



PREFACE TO THE THIRD EDITION. 

The Author desires to express his gratitude to the Profession 
for their very cordial reception of his Work, as well as to the several 
Faculties who have already adopted it, as a text-book in their 
Colleges. 

He has endeavored to eliminate from the present Edition all 
typographical errors, and otherwise to render it, as far as possible, 
worthy of regard as a Standard Work in its Department. 

New York, March, 1870. 



CONTENTS. 



PART I. 

The Slide Valve — Elementary Principles and General Pro- 
portions 11 



PART II. 

General Proportions Modified by Crank and Piston Connec- 
tion 53 

PART III. 
Adjustable Eccentrics 73 

PART IV 
Link Motions 89 

PART V 

Independent Cut-Off, Clearance, Etc 147 

APPENDIX. 

Formula Relating to Crank and Piston Motions . . . 161 



TRAVEL SCALE. 

Attached to the Back Coyer 



PART I. 



THE SLIDE VALVE 



ELEMENT AEY PRINCIPLES 



AND 



GENERAL PROPORTIONS 



POWER AND WORK 



The fundamental query in designing a steam-engine 
has reference to the power required to accomplish a given 
amount of work. 

The term work, when employed in a mathematical 
sense, signifies the continuous overcoming of an offered 
resistance along a definite path. 

The quantity of work is the product of that resist- 
ance into the space passed over. 

As the standards of weight and distance differ through- 
out the world, the expressions for quantity of work also 
differ. With the English standard of pounds avoirdupois 
and feet, the quantity of work is said to consist of a certain 
number of foot-pounds. But with the French standard 
of weight, the kilogramme (=2.20462 libs, avoirdupois) and 
of distance, the metre (=3.28089 ft.), the expression becomes 
a certain number of kilogrammetres. 

Thus the quantity of work expended in raising a weight 
of 300 lbs. through a vertical height of 10 ft. =3,000 ft. -lbs. 
and that of elevating a weight of 50 kilogrammes to a height 
of 20 metres =1,000 kilogrammetres. The quantity of 
work performed by the steam in the cylinder of an engine, 
equals the mean effective pressure exerted upon the entire 
area of the piston multiplied by the space passed over in a 



12 HOESE POWER 

given time. The interval of time usually taken is one min- 
ute ; hence, if the distance traveled by the piston during a 
single revolution of the crank be multiplied by the number 
of revolutions made per minute, their product will equal 
the required space. 

Suppose, for instance, the mean effective pressure on 
each square inch of a piston, having an area of 1,500 sq. 
ins., is 60 lbs. ; then the total pressure will be 1,500x60 
=90,000 lbs., and if the crank makes 40 revolutions per 
minute, with a piston stroke of 3 ft., the speed of the piston 
becomes 3 ft. x 2 x 40=240 ft. per minute ; consequently the 
quantity of work =90,000 lbs. x240 ft. =21,600,000 ft. -lbs. 



I.-HOBSE POWEE. 

A force capable of raising a weight of 33,000 lbs. one foot 
high in one minute is termed a Horse power. 

The expression originated at the time of the discovery 
of the steam-engine from the necessity which then arose for 
comparing its powers with those of the prevailing motor. 
In its early history this unit had three prefixes — Nominal, 
Indicated, and Actual — derived from the various methods 
of estimating the power. The nominal horse power was 
based on the general practice of the age, which dealt with 
low pressures and slow piston speeds. These quantities 
have of late years been greatly increased and the old 
formula in consequence, grown of less and less importance 
as a true expression of relative capacity. 

Indicated horse power designates the total unbalanced 
power of an engine employed in overcoming the combined 
resistances of friction and the load. Hence it equals the 
quantity of work performed by the steam in one minute, 



IIOESE POWER. 13 

divided by 33,000. Thus, in the above example, the indi- 
cated horse power equals 

3)21,600 



21,600,000 _ 

> 000 

' VV 654 HP 



33,000 =11 ^ 20 ° 



The mean effective pressure can alone. be determined by 
means of an instrument called the Indicator. 

The Actual or net horse power, expresses the total avail- 
able power of an engine, hence it equals the indicated horse 
power less an amount expended in overcoming the friction. 
The latter has two components, viz : the power required to 
run the engine, detached from its load, at the normal speed, 
and that required when it is connected with its load. It is 
customary in designing massive engines — in the absence 
of reliable data — to estimate the loss of available pressure 
by the unloaded friction at 2 lbs. per square inch, and sub- 
sequently to deduct 7£ per cent, for the friction of the 
load. Thus, if the mean pressure of the steam within the 

cylinder =60 ^ff" 

2 
It becomes 58 after allowing for unloaded friction, 58 

And 1\ % of this for the friction of the load = 4.4 

Gives a net pressure of 53.6 ib 8 . 

But for small engines of the ordinary design the total loss 
by friction will, in many instances, amount to 15 or 20 % of 
the mean pressure. 

Thus, if the mean pressure =60 lbs. 

15 % of 60 = total loss by friction =_9 " 

Gives an available pressure of. 51 " 



The French apply the term Force de clieval to a 
power capable of raising 4,500 kilogrammes 1 metre high 



14 



MEAN EFFECTIVE PEESSUKE, 



in 1 minute. Reducing these quantities to their equiva- 
lents in pounds and feet and multiplying together, we find 
that their horse-power equals a force capable of raising 
32,549 lbs. 1 foot high in a minute, which is about Y \ less 
than the English unit of measure. 

The following Table furnishes the Force de cheval 
equivalents of horse powers ranging between 10 and 100 : 



Horse Power. 


Force de cheval. 


Horse Power. 


Force de cheval. 


IO 


IO.I4 


60 


60.83 


i5 


I5.20 


65 


65.89 


20 


20.28 


70 


70.97 


25 


2 5-34 


75 


76.03 


30 


30.41 


80 


8l.II 


35 


35-48 


85 


86.17 


40 


40.55 


90 


9I.25 


45 


45.62 


95 


96.31 


5o 


50.69 


100 


IOI.3856 


55 


55-75 


• • 


. . . 



For powers greater than 100, and less than 1,000, multi- 
ply these terms by 10 ; or, if in excess of 1,000, multiply 
by 100. 



II -MEAN EFFECTIVE PRESSURE. 

The character of the connections between the boiler and 
steam cylinder, their length, degree of protection, number 
of bends, shape of valves, etc., must all be considered in 
forming an estimate of the initial steam pressure in the cyl- 
inder ; while the mean effective pressure will depend upon 
the point of cut-off of the steam, and the freedom with 
which it exhausts. 

The exact portion of the stroke that should be completed 
before this closure or cut-off takes place is a vexed question 
among engineers, and its discussion is foreign to the object 
of this Treatise, in which— with the exception of noting cer- 



MEAN EFFECTIVE PRESSURE. 



15 



tain limits prescribed by different valve motions — it will be 
considered as predetermined. 

Having chosen a point of cut-off, and having estimated 
the initial pressure of the steam for a given boiler pressure, 
the question of mean pressure exerted by the steam through- 
out the piston's stroke, can be approximately solved by 
the subjoined Table, which has been computed in the ordi- 



Mean. Pressure, Volume, and Temperature Table. 



£ 




i 








STROKE = 








3 

10 

<o 


V 

3 . 
§ 


> 
> 




MEAN PRESSURE FOR VARIOUS CUT-OFFS. 




ior 


1 or 


J or 


1 or 


| or 


J or 


g or 


'£ 


<U 


0.25 


0.S75 


0.5 


0.625 


0.666 


0:75 


0.875 


Lbs. 


Deg. 




Lbs. 






Lbs. 






Lbs. 


20 


260 


765 


II.9 


14.9 


16.9 


18.4 


18.7 


J 9-3 


I9.8 


25 


267 


677 


T4.9 


18.6 


21.2 


23- 


2 3-3 


24.1 


24.7 


3° 


274 


608 


I7.9 


23-3 


25-4 


27.6 


28. 


28.9 


29.7 


35 


281 


552 


20.9 


26. 


29.6 


32.1 


32.7 


33-7 


34-6 


40 


287 


506 


23-9 


29.7 


33-9 


36.8 


37-3 


38.5 


39-6 


45 


293 


467 


26.8 


33-4 


38.1 


41.3 


42. 


43-4 


44-5 


5o 


298 


434 


29.8 


37-i 


42.3 


45-9 


46.7 


48.2 


49-5 


55 


3°3 


406 


32.8 


40.8 


46.6 


5o.5 


5i-3 


53- 


54-4 


60 


308 


38i 


35-8 


44-5 


50.8 


55-i 


56. 


57-8 


59-4 


65 


312 


359 


38.8 


48.2 


55- 


59-7 


60.7 


62.6 


64.3 


70 


316 


34o 


41.7 


52. 


59-3 


64-3 


65-3 


67.5 


69-3 


75 


320 


323 


44-7 


55-7 


63-5 


68.9 


69.9 


72.3 


74.2 


80 


324 


307 


47-7 


59-4 


67.7 


73-5 


74.6 


77.1 


79.2 


85 


328 


293 


5o-7 


63.1 


71.9 


78.1 


79-3 


81.9 


84.1 


90 


332 


281 


53-7 


66.8 


76.2 


82.7 


84. 


86.7 


89.1 


95 


335 


269, 


56.7 


7o-5 


80.4 


87-3 


88.7 


91.6 


94. 


100 


338 


2 59^ 


59-7 


74.2 


84.6 


91.9 


93-3 


96.4 


99. 


105 


34i 


249 


62.6 


77-9 


88.9 


96.5 


97-9 


IOI.I 


103.9 


1 10 


344 


239 


65.6 


81.6 


93-i 


IOI.I 


101.6 


105.9 


108.9 


"5 


347 


231 


68.6 


85.3 


97-4 


105.6 


106.3 


1 10.8 


113.8 


120 


35o 


223 


71.6 


89. 


101.6 


1 1 0.2 


110.9 


115. 6 


118.8 


"5 


353 


216 


74.6 


92.7 


105.8 


114.8 


115. 6 


120.5 


123.7 


130 


356 


209 


77.6 


96.4 


no. 


119.4 


120.3 


125.3 


128.7 


J 35 


358 


203 


80.6 


1 00. 1 


114.2 


124. 


125. 


130.1 


133-6 


140 


360 


197 


83-5 


103.8 


118.5 


128.6 


130.6 


r 34-9 


138.6 


145 


3^3 


191 


86.5 


io7-5 


122.7 


I 33- 2 


*35-3 


x 39-7 


143-5 


x 5° 


365 


186 


89-5 


in. 2 


126.9 


137-8 


140. 


144-5 


148.5 


. 1 

Common difference . ; 


3.0 


3-7 


4.2 


4-6 


4-7 


~4~8 


5.o 



16 



MEAN EFFECTIVE PEESSUEE. 



nary manner with the aid of logarithms (JSaperian Base). 
The first column is given for pressures above that of the 
atmosphere, or the same as registered by an ordinary 
steam-gauge. The second and third, for temperature and 
volume, are taken from Mons. Eegnault's Experiments 
on Saturated Steam. In the estimate for volume, that of 
the water producing the steam was considered equal to 
Unity. The Table makes no allowance for clearance. 

If from the mean pressure we subtract the mean value 
of the back pressure, or that which may arise from imper- 
fections in the exhaust, which is usually taken for low- 
pressure engines at from 1 to 2 lbs. per square inch, the 
resulting pressure will be the mean effective pressure (in 
pounds) exerted on each square inch of the piston and may 
be represented by the letter P. 

For high-pressure engines (having an ordinary slide 
valve) a more exact determination of the mean effective 
pressure may be secured from the subjoined table, which 
embodies the results of 50 experiments made by Mr. Gooch, 
in 1851, with the locomotive "Great Britain," whose boiler 
pressure varied from 60 to 150 lbs. per square inch. 



Mean Effective Pressures incident to a Simple Slide- Valve Motio?i for 

various Cut-offs. 



Cut-Off at— 


Mean Pressure. 
(Boiler press. = i.oo.) 


Cut-Off at— 


Mean Pressure. 
(Boiler press. = i.oo.) 


O.I 


0-I5 


o-45 


O.62 


O.I25=| 


0.2 


0.5 =i 


O.67 


0-I5 


O.24 


o-55 


O.72 


O.I75 
0.2 


O.28 
O.32 


o.625 = § 
o.666=| 


0.79 
O.82 


O.25 =\ 
0.3 


O.4 
O.46 


0.7 
o-75 =1 


O.85 
O.89 


°-333 = l 
o-375=i 


O.5 =i 

°-55 


0.8 

o.875 = l 


0.93 
O.98 


0.4 


°-57 







SPEED OF PISTON. 17 

EXAMPLE. 

j Boiler pressure = 70 lbs. per sq. in. 
( Steam cut off at § of the stroke. 
Required.— -The mean effective pressure P ? 

We learn from the table that this pressure for a cut-off 
of f the stroke is 0.82 of the boiler pressure. 

Then 70x0.82 = 57.4, or 
The mean effective pressure P = 57.4 lbs. per sq. in. 



III.-SPEED OF PISTON. 

The speed S, or number of feet travelled by the piston 
in one minute, like the subject of cut-off, rests with the 
judgment of the individual designer. Nothing more will 
be attempted in this connection than the presentation of 
quantities most frequently found in ordinary practice : 

Small stationary engines from 170 to 230 ft. per min. 

Large stationary engines 250 to 300 " 

(Rarely as high as 350 ft.) 

River and Sound steamer engines 350 to 500 " 

Marine engines 250 to 600 " 

The Corliss stationary engine 400 to 500 " 

(Usually 50 revolutions.) 
Locomotive engines about 600 " 

(Occasionally 700 or 800 ft.) 
The Allen engine 600 to 800 " 

(Generally the former speed.) 

It is interesting to note that a fine specimen of the latter 
2 • 



18 DIAMETEK OF PISTON. 

form of engine was operated successfully by Mr. Charles T. 
Porter, during the late ''Exposition Universelle," at the 
astonishing speed of 1,400 feet per minute. 



IV.-DIAMETEE OF PISTOL. 

Having decided the questions relating to indicated horse 
power, mean available pressure P and piston speed S, all 
the elements are at hand for determining the area of the 
piston, and consequently its diameter. 

The formula for indicated horse power, solved with ref- 
erence to such area, will read : 

. _ 33, 000 x Horse power 
A - S^P 

or, Area of piston is found by multiplying the required 
indicated horse power by 33,000, and dividing the pro- 
duct by speed of piston multiplied by the mean available 
pressure. 

The corresponding diameter can be obtained from an 
Area Table. 

EXAMPLE. 

Suppose that the indicated horse power =100. 
Piston speed =300 ft. per minute. 
Mean available pressure =21 lbs. 
Then the 

33,000x100 _ oc 

Area= -300^T- =523 - 8s( l- in - 
Which gives a diameter of about 26 inches. 



STROKE OF PISTON. 19 



V-STEOKE OF PISTOL. 

The general expression for the stroke of an engine (in 
feet) is, 



Strokes J^fogJ-P-ggg 



2xNo. of Revolutions' 
conversely, 

No. of Reyolntion S =. F ^ to ° S P eed . 

2 x Stroke 

There are many circnmstances tending to limit the 
stroke of a piston. Among other considerations the diam- 
eter of a paddle-wheel influences the number of revolutions 
that can advantageously be made by the crank of a side- 
wheel steamer, and consequently determines the stroke 
when the piston speed is chosen. Peculiarities of design 
frequently make it desirable that an engine should be run 
at a slow speed and transmit its power through gearing. 

Again, the diameters of pulleys for shafting exert an 
influence, as when the main shaft of a shop is required to 
run at 120 revolutions per minute, then 60 revolutions for 
the crank of the engine, will allow a ratio of 2 : 1 between 
the diameter of the band wheel and shaft pulley. 

With a very rapid piston speed, the stroke of the engine 
is due more to a length imposed on the connecting rod by 
the necessities of the design, than to the number of revolu- 
tions of the crank. In the case of the locomotive, the 
stroke is generally about 24 inches, and the piston speed 
600 feet per minute, while the speed of the engine which 
depends on its power and the diameter of its drivers, ranges 
between 20 and 60 miles per hour. 

The accompanying table has been calculated, for drivers 
of different diameters, to represent the number of revolu- 



20 



STEOKE OF PISTON". 



tions they will make per minute, irrespective of slip, when 
the engine travels at given speeds per hour. 

Revolutions made by Driving Wheels of Locomotive at given speeds. 



Driving-wheel diam- 


SPEED IN MILES PER HOUR. 


Revolu- 














tions 


eter. 


20 miles. 


25. 


30. 


35. 


40. 


50. 


per mile. 


4 ft. o in. 


I40 


175 


210 








420. 


4 " 3 " 


132 


165 


198 






V 


395-5 


4 " 6 " 


124 


156 


186 






■g 


373-6 


4 " 9 " 


Il8 


148 


177 


207 




u 


354- 


5 " o " 


<u 


140 


168 


196 






336- 


5 " 3 " 


3 
C 


i34 


160 


187 




.2 


320.2 


5 " 6 " 


s 


128 


153 


179 


204 


"0 


3°5-9 


5 " 9 " 


0. 




146 


170 


195 




292.3 


6 " o " 


a 




140 


163 


187 




280.3 


6 " 3 " 


3 




135 


157 


179 


224 


269. 


6 " 6 " 







129 


150 


172 


2l6 


258.6 


7 " o " 


ti 




120 


140 


160 


200 


240. 



The subjoined table is applicable to stationary and 
marine engines : 

No. of Revolutions of Crank for Given Stroke and (approximate) 

Piston Speed. 



Stroke. 


PISTON SPEED. 


Ft. 












Ft. 
















Ft. J 




200 


&70 


220 


225 


230 


24.0 


250 


260 


270 


280 


290 


300 


320 


SjO 


350\ 


i ft. 6 in 


67 


70 


13 


75 


76 


80 


S3 


86 


90 


93 


97 


100 


106 


113 


116 


1 " 8 " 


60 


63 


66 


68 


70 


72 


75 


78 


81 


84 


87 


90 


96 


100 


105 


1 "10 " 


55 


57 


60 


61 


63 


66 


68 


7i 


74 


76 


79 


82 


88 


93 


96 


2 " " 


50 


52 


55 


56 


57 


60 


63 


65 


67 


70 


72 


75 


80 


85 


87 


2 " 3 " 


44 


47 


49 


5o 


5 1 


53 


55 


5« 


60 


62 


64 


66 


72 


76 


78 


2 " 6 " 


40 


42 


44 


45 


46 


48 


50 


52 


54 


56 


58 


60 


64 


68 


70 


2 " 9 " 


36 


3« 


40 


41 


42 


43 


45 


47 


49 


5 1 


53 


55 


58 


62 


64 


3 " " 


33 


35 


36 


37 


3* 


40 


42 


43 


45 


47 


48 


50 


53 


56 


58 


3 " 3 " 


3 1 


32 


33 


34 


35 


37 


3« 


40 


41 


43 


44 


46 


5o 


52 


54 


3 " 6 " 


29 


30 


3i 


32 


33 


34 


36 


37 


38 


40 


4i 


43 


46 


48 


50 


3 " 9 " 


27 


28 


29 


3° 


3 1 


32 


33 


34 


36 


37 


39 


40 


43 


45 


47 


4 " " 


25 


26 


27 


28 


29 


3° 


3 1 


3* 


34 


35 


36 


38 


40 


42 


44 


4 " 3 " 


23 


24 


25 


26 


27 


28 


29 


3° 


32 


33 


34 


35 


3« 


40 


4i 


4 " 6 « 


22 


23 


24 


25 


26 


27 


28 


29 


30 


3i 


32 


33 


35 


38 


39 


4 " 9 " 


21 


22 


23 


23 


24 


25 


26 


27 


28 


29 


3° 


3 1 


33 


36 


37 


5 " " 


20 


21 


22 


22 


23 


24 


25 


26 


27 


28 


29 


3° 


32 


34 


35 



AREA OF STEAM PORT. 21 

These dimensions, the stroke of piston and diameter of 
cylinder, are so constantly nsed in comparing engines of 
different powers, that, as far as possible, they shonld consist 
of whole numbers quite free from all fractions of an inch. 



YL-AEEA OF STEAM POET. 

This dimension ranks next to cut-off in its controlling 
influence upon the proportions of the valve seat and face. 
It may justly be considered as a Base from which all the 
other dimensions are derived in conformity with certain 
laws. Its value depends greatly upon the manner in which 
the port is employed, whether simply for admitting the 
steam to the cylinder, or for purposes both of admission 
and exit. In cases of admission it is evident that the pres- 
sure will be sustained at substantially a constant quantity 
by the flow of steam from the boiler. But in cases of exit 
or exhaust, a limited quantity of steam, impelled by a con- 
stantly diminishing pressure, forces its way into the atmo- 
sphere with less and less velocity. If, then, the engine is 
supplied with two steam and two exhaust passages, the 
ports will be correctly proportioned when the areas of the 
latter exceed those of the former by an amount indicated 
by careful experiment. When, however, one passage per- 
forms both duties, it should have an area suitable for the 
exhaust and be opened only a limited amount for the 
admission of the steam. Very excellent results have been 
found to attend the employment of an area equal to 0.04 
of that of the piston, and a steam-pipe area of 0.025 of the 
same, when the speed of the piston does not exceed 200 ft. 



22 



AEEA OF STEAM POET 



per minute, but widely-different factors are demanded by 
higher speeds, like those peculiar to locomotives. 

In the year 1844 M. M. Gouin and Le Chatelier insti- 
tuted a series of experiments for ascertaining the value of 
such terms. These were continued about six years later by 
Messrs. Clark, Gooch, and Bertera, upon engines of British 
manufacture. The various results having been collated 
and analyzed by Mr. Clark, were finally presented to the 
public in his valuable work on "Kail way Locomotives." 
From this it appears that with a piston speed of 600 ft. per 
minute, an area of 0.1 that of the piston was found to give 
practically a perfect exhaust, a steam-pipe area of 0.08 a 
free admission of steam to the chest, and a port opening of 
from 0.6 to 0.9 the entire width of the port, depending on 
the humidify of the steam, a free admission to the cylinder. 

The following table has been prepared for intermediate 
speeds of the piston on the assumption that for average 
lengths of pipe the area increases as the speed, and that a 
higher speed is usually attended by increased pressure : 



Speed of Piston. 


Port Area. 


Steam-Pipe Area. 


2 0o feet per minute. 

250 

300 " 

350 " 
400 

450 " 
500 " 

55° " 
600 


.04 area of piston. 

.047 " " 
•05s " " 
.062 
.07 

.077 
.085 
.092 
.1 


.025 area of piston. 

.032 

.039 

.046 

.053 " 

.06 

.067 

.074 " 
.08 



Having determined the area of the steam port, the next 
step will be to resolve it into its factors, length and breadth. 
When a small travel of the valve is essential, the length 
should be made as nearly equal to the diameter of the cyl- 
inder as possible ; then the port area divided by the length, 
furnishes of course the value of the breadth or S in Fig: 1. 



AREA OF STEAM PORT. 23 

TJie extent to which the valve should open this port for the 
admission of the steam will equal from 0.6 to 0.9 of the 
value of 8, and the minimum travel of the valve, that 
which with a given cut-off just opens the steam port the 
amount of this limit. % The maximum travel is governed by 
expediency, the general tendency of an excess over the 
minimum travel is to render the events of the stroke more 
decisive, the cut-off takes place with greater brevity, avoid- 
ing unnecessary wire drawing of the steam and the release 
opens rapidly, affording a more perfect exit. Where the 
travel is small, these good qualities should be secured by 
increasing this term, until the valve gives an opening equal 
to or even greater than the width of the steam port. With 
a large travel no such attempt should be made, since it 
would inevitably sacrifice much work in friction and cause 
a far greater loss than gain. 

EXAMPLE. 

Diameter of a certain piston =26 inches. Area=531. 
Piston speed =350 ft. per minute. 

Required. — Width of steam port, minimum width of 
port opening and diameter of supply steam pipe. 
From the Tables we have : 

Sq. inches. 

Area of steam port =531 x .062=33 sq. inches. 
The length of the port = diameter of cylinder =26". 
And the width=||=1.3 inches or l T 5 g. 
Minimum width of port opening=0.6 xl.3=| inch. 

Sq. inches. 

Area of steam pipe = 531 x. 046 =24. 4 sq. inches. 
Consequently the diameter=5i inches. 

In the Corliss Engine, where the steam is admitted and 
exhausted through different valves, it is customary to give 
the steam passage an area of T V to T V that of the piston, and 
the exhaust an area of from T ^ to ^ Y . 



24 



AREA OF STEAM POET, 



In this connection a few remarks may appropriately be 
made witli reference to the formation of the valve edge and 
the walls of the steam port. The experiments of scientists 
like Weisbach, D' Aubuisson and Koch, prove that the vari- 
ous phenomena of contraction in the^fluid vein observed in 
the flow of water are equally true for gases, the formulae of 
discharge however have slightly different coefficients of 
efflux. The character of the discharge will evidently vary 
with the extent of opening offered by the valve edge, from 
what is termed "discharge through a thin plate" at the 
commencement, to that through a " short tube" with the 
full opening. Fig. 1 illustrates the natural convergence 



Fig. i. 




which takes place in the filaments of the steam vein with 
the common slide valve. If the edge were formed as in 
Fig. 2 the discharge would be much improved and ren- 
dered similar to that which occurs through an ordinary 
" mouth piece." 

The curvature of the valve edge should commence far 



AEEA OF STEAM POET. 



25 



Fig. 2. 







r -\ 






n 



i 









,V 



n 



I i i 



n 



^ 



enough above the rubbing surfaces to permit a limited 
amount of wear without altering the proportion of the parts. 

Every effort should also be made to reduce the amount 
of clearance for the steam and loss of head by friction, to a 
minimum value. Hence the passage from the port to the 
cylinder must be constructed as short as possible, be of 
uniform cross section and bend with easy curves if bending 
is indispensable. 

In the moulding of a cylinder casting, the cores for the 
steam and exhaust passages should be faced with very 
great care, in order to secure surfaces along which the 
steam will flow with perfect freedom. 



PISTON, CRANK 



AND 



YALYE MOTIONS 



In essaying the study of an intricate subject like the 
relative motions of the piston and the ordinary slide valve 
of a steam engine, it is of the utmost importance to first 
divest the parts of all the complicating influences which 
arise from special constructions and present them in such 
simple and elementary forms, that the discovery of the fun- 
damental laws governing their motions may he facilitated. 
If these are clearly defined, the deduction of others adapted 
to special cases will subsequently he accomplished with 
comparative ease. 

The entire series of events which take place within the 
cylinder of an engine, occur when the piston has reached 
definite positions in its complete stroke. It follows since 
there is in practice no fixed limit to the stroke, that an in- 
finite number of such positions may be occupied, and in 
order to express them by a standard which shall apply 
equally to all cases, a unit scale must be adopted. The 
stroke of all pistons therefore will be regarded throughout 
this Treatise as equal to Unity, and their positions at cer- 
tain important periods, as decimal portions of the entire 
stroke. 

If a movable point is caused to travel around a fixed 



PISTON, CRANK AND VALVE MOTIONS 



27 



one, in the same plane, at a constant distance therefrom, it 
will describe a curved line called a circle. For the pur- 
pose of locating any position in the path of the movable 
point, the circle has from remote ages — though, not wisely — 
been divided into 360 equal parts called degrees (360°), each 
degree into 60 minutes and each minute into 60 seconds. 

While the piston of an engine performs a single stroke, 
the crank-pin makes a semi-revolution (180°) about the 
centre of the main shaft, each position of the former conse- 
quently corresponds with some angular position of the 
crank-arm, and if these angles are arranged in a Table we 
can instantly determine therefrom the number of degrees 
over which the pin must pass in order to bring the piston 
to any desired position. 




28 PISTON, CKANK AND VALVE MOTIONS. 



Since the " slotted cross-head" shown in Fig. 3 is the 
only form of connection between the crank-pin and piston, 
in which the piston moves from one extremity of the stroke 
to the other at the same speed as the crank-pin — measured 
on the stroke line — it will answer our purpose for deter- 
mining the fundamental principles of the piston and valve 
motions. The arrangement of the parts are clearly shown 
in the Figure. The crank-pin is surrounded by blocks BB, 
these slide freely up and down the solid frame FH to which 
the piston-rod is welded, so that while the crank-pin ad- 
vances from D to G the block mounts towards F, returns as 
it approaches E and descends towards H on the return 
stroke ED. For convenience, the cylinder will always be 
regarded as lying on the riglit-hand side of the main shaft 
and the point of the crank-pin circle nearest to the cylinder 
as the zero or starting point of the forward stroke. 

TABLE A. 



Piston Position. 


Crank Angle. 


Piston Position. 


Crank Angle. 


Piston Position. 


Crank Angle. 




Deg. 




Deg. 




Deg. 


O.I 


36} 


o.5625 = T 9 <j 


97s 


0813 = 13 


I28J 


0.125=1 


4if 


o.575 


9 8 g 


0.82 


129? 


0-I5 


45f 


0.6 


IOI i 


0.83 


I3 1 ? 


0-175 


49i 


0.625 =1 


104A 


0.84 


X 32,I 


0.2 


53| 


0.65 


I0 7-2 


0.85 


J 34| 


0.225 


56J 


0.666 = ~ 


109A 


0.86 


*3<*3 


O.25 rzrl 


60 


0.68 


iii| 


0.87 


*37i 


O.275 


63 i 


0.687 -jl 


112 


0.875-I 


i3*t 


°-3 


66j 


0.69 


112J 


0.88 


1 39i 


o-3 2 5 


692 


0.7 


Ix 3§ 


0.89 


141* 


°-333 = 3 


7°i 


0.71 


114J 


1 °-9 


x 43' 


°-35 


1 2 l 


0.72 


116J 


0.91 


!45? 


o.375 = l 


75i 


o-73 


"71 


0.92 


x 47s 


0.4 


78 V 


o.74 


n8§ 


°-93 


H9l 


0.425 


8i| 


o.75 =1 


120 


0.94 


i5i| 


o.437 = i\ 


82? 


0.76 


12l| 


o.95 


I54l 


o.45 


8 4 f 


o.77 


I22| 


0.96 


1561 


o.475 


87s 1 


0.78 


I24I 


o.97 


i6oi 


o-5 =2 


90 


o.79 


12 Sh 


0.98 


163? 


0.525 


92I 


0.8 


126] 


0.99 


1 68J 


o.55 

- 


95? 


0.81 


128} 


1. 00 


180" 



PIST0jN t , CRANK AND VALVE MOTIONS. 29 

The foregoing Table furnishes angular positions of the 
crank-arm corresponding with the various points in the 
stroke which may at times be occupied by the piston. 

To illustrate its application, suppose for — 

EXAMPLE. 

The stroke of a certain piston =36 inches. 

Query. — How many degrees will the crank have passed 
over when the piston reaches points respectively 9" and 
23 1" distant from the commencement of its stroke ? 

6)9,00 
1st. ^=6)1.50=0.25 of the stroke. 

Sb 025 

2d. 2 lt=:?|-| 8 =0.649 of the stroke. 

So do 

Then by the Table : 

0.25 of the stroke=an angular passage of 60°. 

0.65 " = " " 107i-° 

Tlie required angles. 



Again : Suppose the stroke of a piston =36", and that 
the crank has passed over 112°. How far will the piston 
have advanced ? 

The Table gives for 112° a piston position of 0.687 of the 
stroke. 

Therefore 0.687 x 36" =24|" the distance advanced by 
the piston while the crank has advanced 112 degrees. 



There is securely fastened to the crank shaft a device 
called an " eccentric," which serves to impart a recipro- 
cating motion to the slide valve. Upon close inspection it 
appears that this is only a mechanical subterfuge for a 
small crank. 

The travel of any valve being small compared with that 



30 PIS TO N, CRANK AND VALVE MOTIONS. 

of its piston, the crank required for its motion has fre- 
quently an arm or "throw" c b shorter than one-half the 
diameter a e of the main shaft, Fig. 4. Hence to avoid cut- 



Fig. 4. 




ting the shaft and the expense of forming the crank c &, the 
pin m, n, and enclosing strap of the rod are greatly en- 
larged until they attain the common diameter M N, the 
former may then be slipped on, and keyed fast to the shaft 
a e. Of course the motion will not be altered by this 
change, but the same reason that led to the adoption of the 
slotted cross head for tracing the piston's progress, now 
compels us to substitute a small slotted cross head and rod 
for the eccentric rod. In the sequel therefore both the 
crank pin and the eccentric pin (or centre of a centre) will 
be considered as transmitting their motions through slotted 
cross-heads to the piston and the valve. (See Fig. 5.) 

The axes of the cylinder and of the valve stem do not 
always pass through the centre of the main shaft. When 
that of the latter lies above and parallel to the former, as 
shown in the figure, some expedient must be adopted for 
carrying the motion of the eccentric pin up from the point 
q in the central plane of the engine to e in that of the valve. 



PISTOL, CRANK A X D VALVE MOTIONS 31 

This is frequently accomplished by aid of a bar qde called 
a "rocker" free to oscillate on its finnly supported axis d. 
The direction of the motion then becomes the reverse of that 
produced by the eccentric pin and if the pins q and e are 
made to operate in vertical slots no irregularity will be 
introduced by this arrangement. 

Having explained* the general features of these control- 
lers of motion, the crank and the eccentric, and having 
resolved them into their elementary forms, we pass to con- 
sider the parts moved and seek the law of their proportions. 

The plain slide valve of a steam-engine is a device by 
which the entrance and exit of the steam is regulated for 
the opposite ends of the cylinder. It is essentially a case 
A, resting on a plane surface c c as seen in cross section in 
Figs. 5 and 11. Through this surface are cut three passages 
S f , S", and E, separated by the partition walls B, B, called 
"bridges." The two former lead to the opposite extremi- 
ties of the cylinder, and the passage E called the "ex- 
haust" leads through an oval pipe to the atmosphere. 
The valve A is sufficiently large to cover both the passages 
S', S", when standing in its neutral position. A second 
case D, D, called the "steam chest," encloses the valve A 
and is secured rigidly to the plane surface c c. Being- 
larger than the valve it leaves over it much unoccupied 
space to which the only entrance is through the aperture F. 
This space is the " reception room" — so to speak — of the 
cylinder ; to it, the steam is admitted from the boiler through 
F and kept in waiting during such times, as the valve in its 
motion completely covers the two ports. 

Figure 5 represents the crank-pin at the zero point of its 
path, the piston at the extremity H of its stroke, the valve 
in the neutral position and all the parts ready for motion. 
A complete revolution of the crank will carry the piston 



32 PISTON, CKANK AND VA LYE MOTIONS. 

forward to K and return it to the starting point H. What- 
ever events take place in the journey from H to K should 
be repeated in the same order on the return route from K 
to H, hence in studying the motion we will seek to render 
it perfect for the trip from H to K and leave the parts when 
the latter point is reached in the same relative positions as 
those occupied for H, so that the one. will become simply a 
counterpart of the other. The first point evident, is that 
the port S' must be opened and again closed for the proper 
admission of the steam during the stroke of the piston from 
II to K ; in other words, while the piston is making one 
entire stroke the valve must accomplish a half and a return 
half of its stroke. Such an operation can only be brought 
about by securing the eccentric pin in the position/ or b on 
a line at right angles to the crank-arm, that of /being suit- 
able for a direction of the crank indicated by the arrow. 

Let us trace the two motions throughout one revolution 
of the crank. Moving it from the zero to the 90° point will 
draw the piston from the position H to the half stroke or 
the line d\ c", will advance the eccentric pin from f to #, 
the rocker from e q to e ] q 1 , the centre of the valve from V 
to V" and completely open the port S'. As the crank pro- 
gresses from 90° to 180° the eccentric pin will travel from 7c 
towards &, gradually closing the port S' and completely 
covering it when the 180° point is reached, thus leaving the 
valve in the same position at the terminus of the stroke that 
it occupied at the commencement. On the return stroke 
from K to H the port S" will in like manner be opened and 
again closed. In thus hastily following the two entrances 
of the steam to the cylinder, we have lost sight of its mode 
of escape after performing the work of forcing along the 
piston. Let us suppose that one revolution has been com- 
pleted and the piston is prepared for a second journey from 



PISTOL, CRANK AND VALVE MOTIONS 33 

the position II. The space J is now filled with steam and 
some passage of escape must be opened. This is provided 
in the port and pipe E, which are thrown into immediate 
communication with the passage S" when the valve com- 
mences its motion, the opening becoming wider and wider 
as the travel progresses, only closing when the piston 
reaches the point K and is ready to receive fresh steam 
through the passage S" for the return stroke. 

Such is a brief outline of the parts and functions of the 
simplest form of slide valve, in which the steam is admitted 
at the commencement of the piston's stroke and not ex- 
cluded until that stroke is completed. 

This arrangement, however, is not attended with econo- 
mic results, for it entirely ignores that remarkable property 
of steam, its elasticity. To render this latent power availa- 
ble, the steam should be admitted during only a portion of 
the piston stroke, the valve should then be closed and the 
confined volume of steam allowed to complete the remain- 
ing portion, by developing its power of expansion. 

But how can our elementary form of valve and position 
of eccentric be modified for attaining this desirable result ? 

Suppose a cut-off were required at a piston position of 
0.93 of the stroke. By carrying the crank to the 150 J posi- 
tion (as in Fig. 6) we observe that the port S remains 
opened a distance I and the most ready means for effecting 
its closure is to lengthen the valve face by this amount. 
Since the cut-off must take place at relatively the same 
piston position in both strokes, an equal addition must be 
made to the other edge of the valve. Such additions to the 
outer edges of the valve, for the purposes of cut-off, are 
called overlap or simply " lap." The extent of this lap in 
the present case is evidently equal to the horizontal dis- 
tance of the eccentric's centre/" from the 90° line, because 
3 



34 PISTON, CKANK AND VALVE MOTIONS. 

without lap it would naturally close at this line. The same 
distance expressed in degrees would be equivalent to a 
"lap angle" of 30°. 

But on referring to Fig. 6 it is clear that no such addi- 
tion can be made without necessitating a change also in the 
eccentric location, for it would render the admission 30° too 
late. Hence if we add a lap to the valve equivalent to an 
eccentric motion of 30° from its neutral position, we must at 
the same time unkey the eccentric, and having advanced it 
also 30° refasten it on the main shaft. The number of de- 
grees by which the eccentric is thus carried forward from a 
position at right angles to the crank-arm is termed the 
"angular advance" of the eccentric. 

When the eccentric stands at right angles to the crank 
the exhaust closes and release commences at the extremi- 
ties of the stroke, consequently if the eccentric be moved 
ahead 30° not only will the cut-off take place 30° earlier, or 
at a crank angle of 120° instead of 150°, but the release as 
well as the exhaust will take place 30° earlier or at the 150° 
crank angle. Although we have not secured by this pro- 
cess the cut-off aimed at, yet the investigation distinctly 
points out the means at our command for the accomplish- 
ment of any cut-off and will enable us to construct a Scale 
for determining the magnitudes of such alterations. For a 
cut-off of 140° there would be required an angular advance 
of 20° and a lap equivalent to the distance these degrees 
remove the eccentric centre from the line at right angles to 
the crank ; for a cut-off of 160°, an advance of 10° with a 
corresponding lap, and so on ; the exhaust closure taking 
place respectively at the 160° and 170° crank angles. 

This closure of the exhaust confines the steam in the cyl- 
inder until the port is again opened for the return stroke ; 
consequently the piston in its progress will meet with in- 







w 



FIGURE 5 



* 




PISTON, CRAIK AND VALVE MOTIONS. 35 

creasing resistance from the steam which it thus comprc 
into a less and less volume. Such opposition when prop- 
erly proportioned aids in overcoming the momentum stored 
up in the reciprocating parts and tends to bring them 
economically to a state of rest at the end of each stroke. 
Since the closure of one port is simultaneous with the open- 
ing of the other, a release will take place of the steam 
which was previously impelling the piston. Within cer- 
tain limits this also is conducive to a perfect action of the 
parts, for an early release enables a greater portion of the 
steam to escape before the return stroke commences, where- 
as a release at the end of the stroke would be attended by 
a resistance of the piston's progress, from the simple fact 
that steam cannot escape instantaneously through a small 
passage, but requires a certain definite portion of time de- 
pendent on the area of the opening and the pressure. The 
larger the opening then the less the occasion for antici- 
pating the moment of exhaust. 

We learn therefore that the moments of exhaust closure 
and release are, when the valve has neither "inside lap" 
nor its converse " inside clearance" directly dependent 
upon the angular advance of the eccentric, and that an an- 
gular advance of 20° produces a closure at a crank angle 
of 160°, one of 30° at 150° and so on, the resistance becom- 
ing continually greater as the angular advances increase. 
A limit at length is reached where this resistance really 
becomes detrimental, and an amount of power is absorbed 
quite inconsistent with economy of action. On this account 
the single eccentric is rarely used to effect cut-offs of less 
than | the stroke. Earlier cut-offs require two valves and 
two eccentrics, the one set for regulating the cut-off of the 
steam, the other its admission and escape. This subject 
will be more fully discussed in Part V. 



36 PISTON, CEANK AND VALVE MOTIONS. 

The principles just developed can be embodied in a sin- 
gle Diagram called the Travel Scale, whose construction 
is illustrated by Fig. 7. 



Fig. 7. 



# cc ' «• 




*M EXHAUST CLOSURE ANGLES. 



180 CUT OFF ANGLES 



To the Reader.— A. Cop- 
per-plate engraving of the 
TRAVEL SCALE will be 
found attached to the back 
eovcr. 



CEANK AND VALVE MOTIONS. 37 

Let EFD represent the path traversed by the centre of 
an eccentric whose throw equals 3J inches, consequently 
the travel of its valve =7 inches. Then C F at right angles 
to DE will be the normal position of the eccentric from 
which the angular advances must be laid off. Extend this 
line to some convenient point A and join the extremity D 
of the travel with A. Divide the line C A into 7 equal 
parts, and through these points draw lines parallel to D E 
to represent all the travels less than 7 inches. Finally pro- 
ject each degree of the arc D F upon the line D C and join 
the points thus found with the point A. 

The distances from the Base Line C A, at which this 
group of lines intersect the travel lines, will indicate what 
lap should be given to accomplish various cut-offs, and 
their distances from the extreme travel line D A will give 
the width of the steam-port opening due to these travels and 
cut-offs. Thus for 7" travel and a cut-off of 120° the eccen- 
tric must have an angular advance of 30° and the valve a 
lap equal to V C, giving thereby a port opening V D ; while 
a travel of 4 inches with the same cut-off only requires a 
lap of r C 3 and has a port opening of I s d\ The exhaust 
closure of ccmrse takes place in both cases at a crank angle 
of 150, or piston position of 0. 93 the stroke. 

It will be observed that this Scale may be applied with 
perfect accuracy to travels greater than 7 inches by making 
these lines represent their multiples ; for instance, a 4-inch 
travel may stand for one of 8 or 12 inches ; a 6-inch travel 
for one of 12 or 18 inches, and so on. In such cases the 
values of the true lap and lead will be double or thrice 
those given by the Scale. Since the same principle holds 
for travels less than 2 inches, it is clear that the Scale 
must apply to all possible dimensions. 

A slip of paper and a pencil are the only par apliernalia 
of the Travel Scale. To illustrate its use take for — 



33 PISTON, CRANK AND VALVE MOTIONS. 

EXAMPLE. 

Extreme width of port opening must =1 J inches and the 
valve must cut off steam at 0.82 the stroke. 

Required. — Angular advance of the eccentric, travel of 
valve, lap and point of exhaust closure. 

Table A gives for a piston position of 0.82 the stroke a 
crank angle of 130°, for this cut-off an angular advance of 
25° will be required (see line C D of the Travel Scale). 

Apply the edge of a slip of paper to the Inch Scale and 
mark off the desired width of the port opening a, b, as in 

Fig. 8. 

„ ANGULAR ADVANCE. 
90 25° Q° 



4% TRAVEL 



PORT OPENING. 

-- m -- 



-LAP 



cut off= no 

[ EX HA US T CL OSURE = 155 



15 
16 



Carry the same to the Travel Scale, place the mark a 
over the 90° line C A and slide the edge — parallel to the 
line C D— until the mark b stands directly over the 25° an- 
gular advance or lap-angle line. The 4| inches line of 
travel, upon which the slip of paper here stops, will be the 
correct travel for the valve. Before removing the paper 
mark the position c of the Base line. Finally return the 
slip to the Inch Scale and measure the lap b c, which gives 
Jjj of an inch. The exhaust closure on one side and release 
on the other will of course take place at the 155° angle of the 
crank (see line C D) or at a piston position of about 0.95 
of the stroke. 

" Angular Advance =25°. 
Travel of valve =4| inches. 
Lap = if inch. 
I Exhaust closes at 0.95 of the stroke. 
The solution of such problems as the subjoined, will 



Answers. 



DIRECTION OF CRANK MOTION 



39 



tend to familiarize the Reader with the method of using 
this Travel Scale : 

1st. To cut off at | the stroke, with port opening of 1 j- 
inches. 

Required. — Angular advance of the eccentric, travel of 
valve, lap and point of exhaust closure. 

2d. To cut off at | the stroke, with port opening uf If ins. 

3d. " " | " " " " " 3 " 

' 4th. " " 0.7 " " " " " 



13 L< 

16 



DIKECTIO^ OF CEAIK MOTION. 

The direction of any crank motion depends on two con- 
ditions — 1st. The presence or absence of a rocker for trans- 
mitting the motion ; 2d. The location of the angular ad- 
vance with reference to the central line of the valve motion. 
Both of these may be conveniently expressed in a single 
Diagram like the accompanying Fig. 9, in which the posi- 

Fig. 9. 




tive sign (+) represents a motion in the direction of the 
hands of a watch, the negative (— ) a reverse motion. To 



40 L EA D . 

produce a positive motion in any engine, whose eccentric 
acts through a rocker, lay off the angular advance from the 
line bf in the 1st quadrant (the crank standing at the zero), 
but for one without a rocker, the angular advance must be 
laid off from the same line in the 3d quadrant. The 4th 
and 2d quadrants in like manner belong to the negative 
motion. The reason for making such a disposition of the 
angular advance will at once appear upon tracing out 
either of these motions. 

When the power of an engine is transmitted through a 
wide belt to the machinery, the direction of, its crank mo- 
tion will be determined by the relative locations of the 
main and crank shafts. The strain should invariably be 
made to fall upon the lower portion of the belt, the upper 
being thereby relaxed, sags upon its pulleys, increases the 
frictional surface, and materially improves the adhesion of 
the belt. 



LEAD. 

This term is applied to an alteration made in the plan 
of the valve motion for the purpose of concealing and neu- 
tralizing an effect, due to imperfect workmanship as well as 
continual wear in the boxes of the crank and cross head 
pins. The difficulty may be best explained with the as- 
sistance of Fig. 10. 

Suppose, for instance, both boxes of the connecting rod 
A B, fit loosely upon the crank and cross-head pins, that the 
crank moving in the direction indicated by the arrow, has 
reached a location C A within 8 degrees of the zero, and that 
the piston (on account of the lost motion in the boxes) falls 
short of its true position B, a distance B B. If now the 



LEAD 



41 



momentum of the motor carries the crank- pin past its zero, 
the piston, which at the moment of passage is no longer 
urged or restrained by the connecting rod, will by virtue 



Fig. 10. 




of its own momentum continue moving in the direction of 
H until all the lost motion being expended, its progress is 
suddenly checked and it is itself again brought under the 
control of the connecting rod, which then draws it forward 
upon the return stroke. These concussions are reproduced 
at the end of each stroke with a degree of force and sound 
directly dependent on the extent of the lost motion and the 
momentum of the piston with its connecting rod. Where 
the parts are of great weight, as in a marine engine, the 
sound becomes very loud and the engine is said to 
' ' thump " or < 'p>° unci "on the ' ' centres. ' ' Two ways pre 
sent themselves for counteracting this effect ; the one, by 
making the boxes so durable and the workmanship so per- 
fect that lost motion becomes almost impossible ; the other, 
by introducing a resistance to the momentum of the piston 
capable of completely overcoming it before the end of the 
s'roke, in other words by allowing the steam to enter the 
cylinder a short time previous to the termination of the 
stroke. With small engines the first method is practicably 
but in large ones both are more commonly employed be- 



42 LEAD. 

cause with these, a very small amount of lost motion suf- 
fices to produce a disagreeable sound. 

The width of port opening given by any valve at the 
moment its crank passes either centre, is called the " lead" 
of the valve ; and the angular distance of the crank from 
its zero at the instant this opening commences, the "lead 
angle" 

The opening together with the angle (or time) limit the 
power of the steam in its effect upon the lost motion ; for 
even a small opening continued through a long time may 
prove as efficient for the admission as a large opening 
during a very short time. 

Since sound, the effect of lost motion, depends upon the 
weight and velocity of the reciprocating parts, the lead re- 
quisite must vary for different engines and also for the 
same engines at different velocities. The exact amount can- 
not he predicated in any particular case, but after the en- 
gine has been constructed it may be experimentally deter- 
mined by gradually increasing the angular advance of the 
eccentric until some position is found which results in a 
smooth and noiseless movement of the reciprocating parts. 
We have before alluded to the effect of compression by a 
premature closure of the exhaust, but it must be distinctly 
understood that this agency unassisted cannot neutralize 
the evils of lost motion without injuring the admission 
of the return stroke. In this respect it differs from lead. 
It should then usually be supplemented by lead in order 
to accomplish a smooth action of the parts and free opening 
of the steam port for the return stroke. Observe also, that 
so long as the lead angle amounts to only a few degrees no 
impression can be produced on the continuity of the crank 
motion, for the lever arm will be too small for the power to 
exert any influence over the crank. 



LEAD. 

The limits of the lead angle are commonly zero and 8° 
for stationary engines ; while for any given angle the 
width of opening will depend upon the travel of the valve 
and the point of its cut-off. 

It remains to be shown that the Travel Scale is quite as 
applicable to valves having a certain lead as to those with- 
out any. Referring again to Fig. 6, imagine an increase 
in its angular advance of 5°, the valve will then close at 
115° instead of 120° and reopen its port 5° before the crank 
reaches the extremity of the stroke ; but if the lap be re- 
duced 5° when the angular advance is increased 5°, 
the cut off will still remain 120°, while the port com- 
mences to open 10° before the end of the stroke. Con- 
sequently if we wish to arrange a valve for a certain 
number of degrees lead, without altering the point of cut- 
off, it will simply be necessary to find the angular advance 
for a valve without lead, add \ the lead angle for a new 
angular advance, and subtract the other \ for an angle by 
which to measure the lap. 

If in the Example of Fig. 8 a lead of 8 degrees had been 
required, with the same cut-off, the angular advance 
j would have become 25°+4°=29 c 
( and the lap angle 25°-4° =21 ( 
and by applying the port opening marks a and b to the 90° 
and 21° lines, — instead of the 90° and 25° lines, — we 
would have obtained a travel of 3£ inches and a lap of \\ 
inch ; while the distance between the angular advance line 
of 29° and the lap angle line of 21° would have equaled \ 
inch, the width of the lead opening at the extremity of the 
piston stroke. 

The change in the angular advance of course changes 
the exhaust closure from 155° to 151° or about 0.93 of the 
piston's stroke. 






44 LEAD. 

Supposing then a lead angle of 8° for the same problem 
the answers "become : — 

Angular Advance =29°. 

Lap angle =21°. 

Travel =3| inches. 

Lap —\l inch. 

Lead =] inch. 

Exhaust closes at 0.93 of the stroke. 



Similar suppositions made and applied to the other trial 
problems will give all the practice requisite for successfully 
using the Travel Scale. 

It seems almost unnecessary to observe that the Scale 
effects with equal readiness and precision solutions 
directly the converse of that just accomplished. Thus, 
if the above lap, lead and travel were given, to determine 
the exhaust closure and cut-off, we would mark the lap and 
lead on a strip of paper as in Fig. 12, apply the same to the 
3 1 inch travel line of the scale, which would show at once 
an angular advance of 29° and consequently exhaust 
closure of 0.93 the stroke ; also a lap angle of 21° with 
lead, or 25° without, the same as a cut-off of 130° =0.82 
the entire stroke. 

A moment's reflection will also show that — during the 
progress of the crank — the varying width of the port open- 
ing from the simple lead out to the maximum width and 
back again to the period of cut-off, might readily be traced 
on the Scale, and all the information common to the popu- 
lar method of ellipse or other construction, be immediately 
obtained. But the facts thus gained, would prove of very 
trifling moment, so long as the valve had received a correct 
maximum port opening. 




Fig. 11. 



i 

t \ 
1 \ 

1 \ 
1 \ 

> 1 

1 1 


I J NEUTRAL POSITION. \% 

i 

i / 
i / 
; / 

! 

/ 

y 

,4— -"■'' 



To toe Reader.— C«< MlS 
/>Z<7te i« tivo through C C the 
line of the Valve Face . 

By sliding the valve piece 
back and forth over its ports, a 
very clear idea will be obtained 
of the relative positions of the 
edges during motion. 



WIDTH OF BRIDGE. 47 

WIDTH OF BBIDGE. 

This dimension is usually made of equal thickness with 
the cylinder, in order to secure a perfect casting, but at 
times it becomes necessary to increase its width. The only 
danger from a narrow bridge is an overtraxel of the valve, 
by which the exhaust passage would be placed in direct 
communication with the "live steam" in the chest, and 
followed by continual waste of the power. Obviously this 
cannot occur while the difference between the port opening 
and the steam port does not exceed the width of the bridge. 
(Fig. 11.) But to prevent even the possibility of aleak- 
age :— 

Add about \ of an inch to the width of the opening and 
from their sum subtract the width of the steam port. 

Thus the width of the steam port in the example of Fig. 
8, should have been at least : — 

li-fi"_l ? ' = iinch. 

When however the width of the opening is less than that 
of the steam port, the danger of such an escape entirely 
vanishes. 



WIDTH OF EXHAUST POET. 

The main difficulty to be avoided in proportioning the 
width of this port is the possibility of a reduction in its 
area, when the valve attains extreme travel, to an opening 
materially less than that of the steam port from which it 
derives its supply. 

Suppose that the valve in Figure 11 has reached the end 
of its half travel, or the exhaust edge V moved a distance 



48 



INSIDE LAP. 



K, from its neutral position V 2 ; then by the above condi- 
tion, E will evidently equal (S + R— B). 
Which furnishes the following general 



RULE 



For determining width of Exhaust port. 
Add the width of the steam port to \ the travel and 
from their sum subtract the width of the bridge. 



When called upon to perform the addition or subtrac- 
tion of many fractional portions of an inch, it will generally 
be found more convenient to express these decimally than 
by those very awkward subdivisions sixty-fourths, thirty- 
seconds, etc. 





Fractions of an inch expressed decimally. 




^L of inch = .0156 


.i + Aof i 


nch = . 3 4 3 8; 


§ + -J g of inch= .6875 


32" 


= .0313 


i " 


= •375 j 


5 *_i_ 3 1 

8 + 32 


- .7188 


1 1 

1 6 


< =.0625 


3 _l 1 It 

S r 3-i 


= .40631 


3 I 


= -75 


3 < 

32 


' =-0938 


3 1 1 it 

8 +T6 


= •4375 


3j. 1 i 
4 + 32 


' = .7813 


i ' 


' =.125 i 


3 1 3 a 

8 T 32 


= .4688 


a 4- jl « 

4 ~ J 6 


' = .8125 


111 ( 

8 + 32 


' —1563 


i_ it 


= •5 ! 


! + 3 3 2 ' 


1 = -8438 


5 + Jg 


' =.1875 


1 4- J a 

2 + 32 


=-53 I 3 


i ' 


' = -875 


k+A ' 


< =.2188 


1 .4- 1 a 

2 ^T6 


-•5625 


14-J- * 
8 r 32 


= -9063 


t ' 


= .25 


I 4- _3 a 

2^32 


= .5938; 


7 1 1 < 
8 +TG 


' ■ = -9375 


4 ~ 3 2 


< =.2813 


5 a 

8 


=•625 ! 


1 4- X < 
8 + 32 


= .9688 


1 4- JL < 

4 + 16 


=•3125! 


1 1 U 

8 + 32" 


=•6563 


i //zr/ 


% =1.000 



I3STSIDE LAP. 

The effect on a valve motion of inside lap is to — 

Prolong the Expansion, and 

Hasten the Compression. 

(A contrary effect for inside clearance.) 



INSIDE LAP 



49 



The former is occasionally added in the case of high- 
speed engines having very late cnt-offs. In such instances 
the compression is arranged to commence at about \ of the 
stroke, or at an angle of 138 degrees, and the release at an 
angle not exceeding 160°. For example, if the angular 
advance equals 32° (with a travel of 4§ inches) the compres- 
sion would commence at a crank angle of 148° or 10° later 
than the above limit ; hence if we give the valve an inside 
lap of 10° or § of an inch found as in Fig. 12, the expan- 

Fig. 12. 



ANGULAR ADVANCE 
S0° 3,2° 26 l 



E*S 



PORT OPENING. 



A- 5 // TRAVEL. 



l/A/S/DE 
V LAP.' 



LAP. 




sion will continue from the point of cut-off to 148° + 10° = 
158 degrees, and the compression commence at 148°— 10°= 
138 degrees, instead of both events taking place at the 148° 
angle of the crank. 



We think the foregoing investigations fully sustain our 
remarking in conclusion that any questions, relating to the 
travel of the valve, the varying widths of the exhaust and 
steam-port openings for every possible position of the 
crank, the moments of closure and release, and other points 
of interest, can not only be determined with perfect pre- 
cision by means of the Tkavel Scale, but their solution 
will prove well nigh instantaneous when compared with 
the indirect and tedious methods that have heretofore ob- 
tained in popular usage. 



50 GENERAL EXAMPLE 



GENERAL EXAMPLE. 

What dimensions should be given to the cylinder and 
valve of an engine like Fig. 5 to secure an indicated horse 
power of 150 with 

Pressure of steam in boiler at 65 lbs. ; 

The crank to make 50 revolutions per minute, and the 
steam to be cut off at § the stroke % 

The mean effective pressure (page 16) =65 x 0.82=53.3 
lbs. Piston speed (page 17)= say 250 ft. per minute. Area 
of piston, page 18, 

. 33,000x150 132x150 ow1 . , 
A = W^53X = -T373-^ 371 ** mcheS ' 

Therefore diameter of piston = 21 f ins., say 22 inches. 

250 
Stroke of piston (page 19) = --—=2. 5 ft. =2 ft. 6 inches. 

Port area (page 22) =371 sq. inches x .047=17.4 sq. inches. 

If the length of the steam port =20 inches then its width 

17 4 
will=-^-=fmch. 

Width of port opening W (by page 23) may vary be- 
tween 0.6 and 0.9 the width of the entire port, but for the 
sake of greater precision in the cut-off and freer opening of 
the port at the commencement of the stroke, let us make its 
width equal about 1.5 width of steam port, or — 

W=1.5x J"=1J inches. 

Area of steam pipe (page 22) =371 sq. inches x. 032= 
11.9 square inches. 

Area of exhaust pipe=area of steam port =17. 4 sq. ins. 

The respective diameters of these pipes will therefore be 
4 and 4| inches. By the Travel Scale, the angular advance 



GENEEAL EXAMPLE. 51 

for the given cut-off of 110° equals (without lead) 35° and 
with a lead angle of say 6°, 

Angular advance will=35° + 3°=38 degrees, 
And lap angle will =35°— 3° = 32 degrees. 

Now apply the width of port opening 1\ inches to the 
90° and 32° lines of the Travel Scale, as page 38, and we 
find that the Travel must=5§ inches. 

After marking the Base line and angular advance we 
have — 

Lap =1^6 inches ; lead = \ inch. 

The bridge, page 47, should not be less than J"'-| 14"—$" 
= | inch. If, however, the cylinder has a thickness of 1 
inch the bridge must be made of the same width. 

Width of exhaust port, page 48, 

E=| + 2f-l"=2f inches. 

Also we have the width of each valve face F and N= width 
of steam port + lap 

Equals, i" + ljb"=2& inches, 

And the total length of the valve or 

L= exhaust port + 2 bridges + 2 faces =2§ + 2+4§=9| 
inches. 

The angular advance being 38° the exhaust will close 
and release commence at the 142° angle of the crank (see 
Travel Scale) or at 0.895 of the stroke = 30" x 0.895 =26$ 
inches and the cut-off take place at |x30"=20 inches; 
which embraces all the required dimensions. 



PART II 



GENERAL PROPORTIONS 



MODIFIED BY 



CRANK AND PISTON CONNECTION 



CKA^K AND PISTOL CONNECTION". 



Thus far we have confined our attention to a form of 
connection called the " slotted cross-head," and have been 
able therewith to deduce laws governing the proportions of 
the various parts of the valve, as well as to devise a most 
simple and rapid method for determining their magnitudes. 
But since this connection seldom obtains in practice, it 
becomes necessary for us to analyze the form shown in Fig. 
13, to modify their general proportions to accord with the 
new conditions and to eliminate as far as possible all the 
irregularities they tend to create. 

It will be observed, by inspecting this Figure, that the 
cross head pin is drawn a distance BB" beyond its half 
stroke position B", when the crank attains an angle of 90°, 
that this irregularity is due to the want of parallelism of 
the connecting rod, with its original position — during the 
progress of the crank pin in its semi-revolution — and that 
a rod of virtually infinite length produces a motion of the 
piston identical with that of the cross-head. It follows 
that the irregularity BB" will vary -with the different ratios 
that may exist between the length of the crank arm and the 
connecting rod. In subsequent comparisons of these two 
terms, the length of the craiik arm will -always be regarded 



56 



C K A N K AND PISTON CONNECTION. 



as the Unit measure and that of the connecting rod as a 
certain number of times the length of the crank arm. 

Let the crank arm C A Ibe equal to unity and the con- 
necting rod A B=4, then their ratio is that of 1 to 4, (1:4.) 
When the arm occupies the 90° position the cross-head pin 
will be drawn a distance B B" beyond the half stroke point 



Fig. 13. 




60 - Us^* - 

SO 37 



B". With B as a centre and A B as radius, describe the 
arc A A". If the occasion required, it might be readily 
proved that A", the point of its intersection with the line 
D E, is the same distance from C that B is from B". Placing 
the crank in other positions — as at 30°, 60°, 120° and so on 
— and describing similar arcs there will result like irregu- 
larities but of a less degree, all of which however vanish 
at the extremities of the stroke D and E. It becomes evident 
therefore that the effect of this form of connection is ; to 
carry the piston ahead of its proper positions throughout 
the forward strolce and on the return stroke to make it lag 
behind the positions due to the locations of the crank pin. 

Consequently the one crank angle, for a given piston 
position (as in Table A), will no longer serve both the 
forward and return strokes, but a new table must be 



CEANK AID PISTON CONNECTION. 57 

constructed which shall furnish at sight the proper angles 
of the crank for various piston positions in both the For- 
ward and the Return strokes, and. these for every important 
ratio of crank to connecting rod between 1 : 4 and 1 : 8 with 
which intermediate values may readily be determined by 
interpolation. Such is presented in the following Stroke 
Table.* 

The fractional portions of a degree have been given as 
small as can conveniently be laid off with a protractor. 

By transposing the terms Forward and Return the 
angles in the Table will apply to the case of a " Back 
Action'''' Engine. For the irregularities of the motion are 
necessarily reversed in such instances, because the cross 
head and cylinder lie on opposite sides of the main shaft 
instead of on the same side. 



FIRST EXAMPLE. 

The connecting rod of a certain engine =8' 3" =99". 

The crank arm =18 inches. 

Cut-off takes place at 0.65 of the stroke. 

Required — The forward and return stroke crank angles. 



Divide length of connecting rod by that of the crank 
arm : thus 

18~" 2 
Their ratio therefore will be that of 1 : 5J.f 

* Tlie trigonometric formulae pertaining to tins Table are furnished in the 
Appendix and angles, for any special case may be found by their aid. 
f A Ratio commonly adopted by the builders of stationary engines. 



58 



CRANK AND PISTON CONNECTION- 



STROKE TABLE. 









CRANK ANGLES. 












(for ORDINARY CONNECTING ROE 


•) 




Piston Position. 


















( Stroke = unity.) 


RATIO 1 : 


4. 


RATIO I : 1-£. 


RATIO 1 : 5. 


Forward 


Return. 


Diff. 


Forward 


Return. 


Diff. 


Forward 


Return. 


Diff. 




deg. 


deg. 


deg. 


deg. 


deg. 


deg. 


deg. 


deg. 


deg. 


O.I25=| 


37! 


46! 


9i 


37s 


A 6\ 


H 


37s 


45S 


7-1 


0.2 


48 


59^ 


JI 3 


48J 


m 


ioi 


4»l 


5«* 


9' 


0-25 =1 


54l 


66| 


I2| 


54^ 


66 


"i 


55i 


65^ 


10 


0.3 


6o| 


73" 


13 


61 


72§ 


"1 


6i,i 


72 


10J 


0-333 = 1 


64J 


77fi 


13! 


64J 


1H 


W 


65! 


76] 


io2 


°-375 = i 


681 


8 2 | 


i3i 


69^ 


82 


121 


7oj 


8i| 


"i 


0.4 


7i| 


85^ 


13? 


7»i 


84^ 


12^ 


73 


841 


"i 


o-45 


77! 


9 1 * 


I4g 


78^ 


' 9°" 


"i 


7^g 


90 


»l 


0.5 =J 

o-55 


82I 


97g 
io 2 | 


I4g 


83 3 ' 
89I 


96] 


I2 i 


84! 


95 S 


"8 


88. ', 


lOlg 


I2A 


90 


IOl| 


1 1| 


0.6 


94| 


108} 


I3» 


95s 


io7§ 


I2l 


95l 


107 


"i 


0.625 = 1 


97i 


mi 


i3i 


98 


110J 


I2j 


981 


io 9 | 


"i 


0.65 


100^ 


ii3s 


i3§ 


IOl| 


"3* 


"1 


lOlf 


II2§ 


i°«J 


o.666=| 


102I 


«sl 


r 3l 


io 3b 


"51 


"* 


103! 


"4b 


»u 


0.68 


104 


«7l 


i3| 


104! 


n6| 


12 


io 5^ 


ii6| 


ioi 


o-7 


106^- 


ir 9i 


13 


i°7l 


119 


«* 


108 


n8i 


io| 


0.71 


io7s 


I20| 


"J 


io8g 


1 20 J 


"1 


io 9 | 


"9? 


log 


o-73 


110A 


"3t 


"1 


iiij 


I22§ 


"1 


112 


122J 


103 


o.75 =1 
0.76 


"3? 

ii4| 


"51 
126J 


"f 
"1 


114 
"5J 


"5b 


II 


"4a 

116I 


"4| 


10 
9l 


126J 


"5b 


0.77 


116I 


I28i 


12 


n6j{ 


"7e" 


io| 


1174 


"7i 


9l 


0.78 


n7| 


I29J 


»i 


n-8| 


128^ 


ioi 


119 


128.1 


9^ 


0.79 


ii9s 


1304- 


"i 


"9s 


x 3oj 


iof 


I20tt 


"91 


9i 


0.8 


I20.' ? 


132 


Hi 


I2l| 


^S 


I°4 A 


I2l| 


^J 


9l 


0.81 


I22± 


1331 


™i' 


I22| 


1324° 


10 


"32 


I3 2 5 


9 


0.82 


I2 3l 


I 34§ 


11 


I24A 


I34l 


94 


125 


133? 


8| 


0.83 


"58 


136 


io| 


126 


1351 


91 


I26§ 


!358 


8} 


0.84 


127 


137^ 


ioi 


"7^ 


137 


9! 


128] 


i36 4 ? 


8i 


0.85 
0.86 


128^ 
T 3°i 


138^- 


10} 


129I 
1313 


I3*i 


9* 


_i30_ 
I3!r 


138I 
i39| 


8] 


Mo| 


9l 


140 


8f 


0.87 


132I 


142 


9i 


i33 


1411 


8| 


!33i 


141? 


7^ 


0.875-I 


i33i 


142J 


9l 


i33l 


I42I 


8^ 


I 34| 


H2| 


71 


0.88 


i34] 


I43A 


9i 


!34t 


i43i 


8 1 , 


I354 1 


142^ 


7g 


0.89 


136^ 


145 1 


9 


i 3 6| 


i44 4 3 


8 


i37t 


144^ 


7^ 


0.9 


138^ 


146? 


8| 


138^ 


i 4 6| 


73 

/4 


I 394 l 


146J 


7 


0.91 


140.5 


i 4 8J 


8 


141 


148] 


7i 


*4*J 


148 


6g 


0.92 


142I 


150,! 


7! 


1435 


i5°8 


6g 


I43s 


i49s 


0! 


o-95 


i5o| 


I56| 


6^ 


*S*i 


156A 


51 


"Si* 


15^5 


4i^ 



CRANK AND PISTON CONNECTION. 



59 



STROKE TABLE. 











CRANK ANGLES. 












(for 


ORDINARY CONNECTING ROD.) 




Piston Position. 
(Stroke=unity.) 


RATIO 1 : 


51. 


RATIO 1 : 


6. 


RATIO 1 : 0|. 


Forwarc 


Return. 


Diff. 


Forwarc 


Return. 


Diff. 


Forward 


Return. 


Diff. 




deg. 


deg. 


deg. 


deg. 


deg. 


deg. 


<&£"• 


deg. 


deg. 


°-I 2 5=S 


38j 


45.! 


7 


sH 


44? 


6] 


38:? 


44^ 


5! 


0.2 


49 i 


57^ 


8] 


49^ 


57.{ 


7| 


49 1 


56f 


7 


O.25 = \ 


55? 


644 


9 


56] 


64J 


83 


5*1 


64 


71 


0.3 


6ig 


7*2 


91 


6 2 | 


7i 


83 


622 


7°g 


8 


o-333 = l 


652 


75s 


9! 


66j 


75] 


9 


66> 


74| 


8s 


0-375^1 


7o| 


8o| 


i°J 


71* 


80] 


93 


7i| 


79s 


8} 


0.4 . 


73^ 


83I 


"I 


73* 


S3-I 


9f 


74.! 


82 \ 


8-5 


o.45 


79^ 


8 9 \ 


10] 


791 


88^ 


9l 


80 


88, i 


8§ 


0.5 =1 
°-55 


»4l 


95» 


io 4 i 


851 

9H 


94| 

ioo| 


9l 


_85f 

9 J b 


94g 

100 


.81 

81 


90 \ 


100^ 


IOJ 


9l 


0.6 


96J 


106^ 


wi 


96? 


io6£ 


93 


97^ 


105? 


8:1 


0.625 = 1 


99i 


io 9 | 


I°J 


99? 


108J 


93 


ioo| 


108^ 


8i 


0.65 


I02 i 


112] 


91 


I02 4 3 


111J 


9 


IQ 3h 


mi 


H 


o.666=l 


io4| 


"4l 


9! 


I0 4 | 


113! 


9 


105-! 


IJ 3b 


K 


0.68 


106J 


"5l 


9l 


I06.] 


"5i 


83 


106^ 


ii5 


K 


0.7 


108.J 


n8| 


9l 


IO9 


"7l 


83 


i°9h 


"7l 


8 


0.71 


i©9s 


"9i 


9j 


nog 


118,3 


8.1 


nof 


n8| 


7i 


o-73 


II2t> 


I2lf 


9-i 


IJ 3 


I2l| 


8| 


Il 3l 


1211 


71 


o-75 =| 
0.76 


"Si 
116J 


124] 

I2 5i 


9 
83 


"5& 

117 


123! 

"5s 


8J 
83 


116 
"7| 


123^ 


7? 
7 5 


I2 4g 


0.77 


118 


126J 


8f 


n8| 


126J 


8 


ii8| 


126J 


7i 


0.78 


"92 


128^ 


si- 


120 


127J 


14 


I20 8 4 


127^ 


7s 


0.79 


121 


129I 


si 


I2lf 


129 


7i 


121^ 


128I 


7 


0.8 


122 i 


130! 


84 1 


122? 


I 3°i 


7l 


I23J 


r 3°4 


7 


0.81 


124 


132 


8 


I24| 


131? 


73 


I2 4 | 


J 3^ 


6^ 


0.82 


125- 


i33i 


8 


126 


^s 


7a 


I26J 


J 3 2 i 


6S 


0.83 


"7b 


x 34f 


7l 


127^ 


J 34' 


7 


I27| 


r 34g 


6^ 


0.84 


128? 


J 3 6 s 


7l 


I29J 


136 


6? 


I 29 I 


J 35.i 


6.i 


0.85 

0.86 


I 3°H 


137? 
*39l 


73 
73 


I3°4 

!3 2 ' 


1372 


6-i 


n 1 ! 
132! 


I 37| 
i38 h 7 


6* 
6 fc 


1324 


139 


6.1 


0.87 


^s 


141 


71 


1344 


i4°| 


63 


134J 


140.] 


6 


o-875=I 


134? 


141? 


7 


I35J 


141J 


6{ 


135] 


141 ! 


5! 


0.88 


135? 


i 42 | 


63 


136] 


J 42 8 3 


63 


136! 


142 j 


5? 


0.89 


i37j 


i44i 


63 


138 


144 


6 


138! 


*43! 


5^ 


09 


i39| 


M5h 


63 


J 4o« 


i45s 


5 5 


i4o h 3 


>4S-i 


5, 


0.91 


i4i| 


H7l 


6 


142I 


i47^ 


53 


142J 


i47j 


5 


0.92 


J 44s 


] 49h 


5-J 


H4| 


149; 


5 


144.3 


T 49l 


45 


o-95 


I5i| 


J 5^ 


4l 


152 


156, 


4 


J 5 2 l 


155? 


3-J 



60 



CRANK AND PISTON CONNECTION. 



STROKE TABLE, 

















1 — 


— — , 










CRANK ANGLES. 






Piston Position. 
( Stroke = unity.) 






(fob 


ORDINARY CONNECTING ROD.) 




RATIO 1 : 


7. 


RATIO 1 : 


7i 


RATIO 1 : 8. 


Forward 


Return. 


Diffi 


Forwarc 


Return. 


Diff. 


Forwarc 


Return. 


Diff. 




deg. 


deg. 


deg. 


deg. 


deg. 


deg. 


deg. 


deg. 


deg. 


O.I25=l 


39 


44] 


51 


39s 


44 


4l 


39i 


43 g 


4? 


0.2 


5o 


56, 


6A 


Sol 


56;! 


6| 


5o| 


56g 


5! 


O.25 = -\ 


56^ 


63 1 


7" 


56! 


63/ i 


6| 


57g 


634 1 


6^ 


°-3 


62 1 


70i 


7i 


63, 


70 


6f 


63 1 


69? 


H 


o--333=4 


661 


74' 


75 


67« 


74] 


7| 


67^ 


74 


6 o 


o.375=l 


7i§ 


79i 


73 


7*1 


79l 


7 5 


72^ 


79s 


i 


0.4 


74i 


82! 


8 


74| 


•82 j 


7i 


75 


82 


7 


o-45 


80] 


881 


8] 


8oi 


88' 


7 2 


8o| 


87! 


7 


0,5 =£ 

o-55 


852 


94g 
99? 


H 


86] 


93! 


7^ 


86g 
92] 


93s 


7 


9 1 ! 


' H 


92 


993 


7i 


99 1 


0.6 


972 


IQ 52 


8 


97! 


105] 


7i 


98 


105 


7 


0.625=1 


IO °h 


108J 


7l 


ioof 


108J 


7i 


100^ 


IC 78 


7 


0.65 


I0 3i 


ni] 


7! 


io 3 | 


no| 


71 


104 


noj 


6? 


o.666=l 


105J 


"3g 


71 


105! 


II2| 


7J 


106 


II2| 


61 


0.68 


io7i 


"4? 


7i 


IC 7i 


"4-J 


7 


107I 


114] 


61 


0.7 


109I 


"7? 


7i 


no 


116? 


61 


no] 


II6J 


61 


0.71 


in 


nSf 


71 


i»l 


n8i 


61 


iii^ 


"7s 


6g 3 


o-73 


II 3l 


I20f 


71 


"3s 


I20| 


6| 


"4g 


120J 


6] 


o.75 =| 


n6| 


I23| 


7 


n6 b 5 


I2 3j 


61 


116J 


I22| 


6g 


0.76 


"7i 


"4i 


7 


"72 


I2 4| 


64 


"8J 


I2 4g 


6 


0.77 


"9g 


126 


61 


"9-J 


125I 


6f 


"9s 


I2 5\> 


5g 


0.78 


I2 °2 


127I 


6| 


I20| 


127 


61 


121 


126? 


5s 1 


0.79 


122 


128J 


61 


122] 


128I 


6 5 


I22 2 


128' 


5l 


0.8 


12 3] 


130 


6| 


I2 3.S 


i2 9 | 


(>i 


I2 3g 


I2 9 § 


5. 


o.8r 


125 


13^ 


6] 


125I 


J 3l8 


6 


1251 


!3ol 


5 5 


0.82 


126^ 


132! 


H 


126I 


J 32o 


K 3 

i 


127 


132] 


5i 


0.83 


128^ 


134] 


6| 


1283 


J 33g 


5i 


1281 


I33f 


54 1 


0.84 


129I 


i35l 


6 


I3O 


T 35i 


5-1 


I 3°l 


1354 


5s 1 


0.85 
0.86 


r 3i| 


i37i 
138J 


s2 


I3.i| 


137 
138^ 


Si l 


J3LJ 

!33i 


136^ 


5 
41 


*33g 


si 


133? 


5} 


*3H 


0.87 


134! 


140] 


s^ 


i35 


Mo^ 


5g 


I 35 4 1 


140 


4f 


o-875 = I 


"135! 


!4l8 


si 


136 


1401 


43 


i36g 


140-J 


4§ 


0.88 


r 36§ 


I42 


51 


!36g 


141! 


4| 


137 


MIg 


4i 


0.89 


138, 


r 43fl 


5] 


138! 


143? 


4| 


138I 


J 43l 


42 


0.9 


140;} 


I45S 


4l 


140J 


*45i 


4i 


140! 


145 


41 


0.91 


i 4 2| 


i47i 


4! 


142! 


J 47s 


43 


143 


147 


4 


0.92 


I 44a 


I49h [ 


4} 


145 


149 


4 


i45g 


149 


3s 


o-95 


152I 


i55l 


3] 


!52n 


J 55l 


3s 


i52g 


i55i 


1 



ECCENTRIC AND VALVE CONNECTION. Gl 

Referring to this Ratio column in the Stroke Table we 
obtain : — 

Crank angle of the forward stroke for the 0.65 position 
=112f°. 

Crank angle of the return stroke for the 0.05 position 
= 122}°. 

Difference between the return and forward =dl°. 



SECOND EXAMPLE. 

Stroke of piston =45 inches. 

Ratio of crank to rod=l : 6£. 

Forward stroke crank angle=131 J°. 

Return stroke crank angle =134§°. 

What locations will the piston occupy for these angles ? 

From the Stroke Table we learn that : — 131 | J forwards 
piston location of 0.85 the stroke and 134 1° return = piston 
location of 0.83 the stroke — consequently : 

45" x 0.85 =38 \ inches from commencement of forward stroke. 
45"x0.83=37f " " " return " 



ECCESTBIC A^D VALVE CO^]SrECTIO^ T . 

The principle of this connection has already been illus- 
trated by Fig. 4, its standard motion in Fig. 5, but as the 
latter rarely occurs in practice it becomes necessary to 
study the former with reference to its influence on the 
events of the valve motion. It has been observed that the 
combination is nothing more nor less, than that of a small 
crank with a long connecting rod, the valve will therefore 
move in precisely the same manner as the piston, and will 
have in its progress from one extremity of the travel to the 



62 LENGTH OF ECCENTEIC EOD. 

opposite, like irregularities, differing only in degree. In 
other words, when the eccentric arrives at the positions for 
cut-off and lead, the valve will be drawn beyond its true 
position — measured towards the eccentric — by a distance 
dependent on the ratio between the throw of the eccentric 
and the length of its rod. Since this difficulty is corrected 
by lengthening the rod, it follows that the width of the 
port opening in one stroke, will slightly exceed that in the 
other. This is practically the only effect produced by the 
use of the true eccentric connection ; although strictly speak- 
ing there is besides a slight difference in the equality of the 
exhaust closure, yet in no case does this become sufficient 
to affect the general action. 

Neither is the difference in the opening appreciable in 
stationary engines, for their ratio of eccentric throw to 
length of rod is usually that of 1 : 20 or 30, which gives a 
variation too small to influence the general admission of the 
steam. (See Example 4 of Appendix.) 



LENGTH OF ECCESTEIC EOD. 

To find this dimension geometrically, after the propor- 
tions of the valve have been determined with the Travel 
Scale, proceed as follows : — 

1st. Map the centre lines of the cylinder, valve, rocker, 
and main shaft. 

2d. Place the crank at the zero and the valve in such a 
position that its edge F (Fig. 11) will give the proper open- 
ing for the forward stroke lead. 

3d. Find the position of the centre of the eccentric by 
laying off the angular advance from the 90° line. Finally 



CORRECT CRANK ANGLE. G3 

measure the distance from this centre to the rocker pin— or 
that of the valve stem as the case may be— for the correct 
length of the eccentric rod. 



COEEECT CEANK ASGLE. 

In finding the travel, lap, etc., of a valve appropriate to 
a given cut-off, by means of the Travel Scale and Stroke 
Table, the Return Stroke crank angle should be inva- 
riably employed. This will result in a correct cut-off for 
the return stroke although a later one than desired in the 
forward stroke. A method of correction for this inequality 
will presently be explained. 



EQUALIZATION OF LEAD OPENING. 

Since the lead opening is measured at the moments 
when the crank pin passes the central line, there can exist 
no irregularity between the piston positions, and if the length 
of the eccentric rod be determined as above the widtli of 
the lead opening in the return stroke will equal that of the 
forward stroke. 



EQUALIZATION OF EXHAUST CLOSUEE. 

The nearer we approach the half stroke positions of the 
piston the greater becomes the inequality between the crank 
angles, and as the uniformity of the exhaust closure and 
cut-off depends directly upon these values, it is evident 



64 EQUALIZATION OF EXHAUST CLOSUEE. 

that they also will prove unequal for the forward and re- 
turn strokes. 

The equalization of the exhaust closure is always possi- 
ble, because for a direct-action engine a small amount of 
inside lap added to the face N (Fig. 11) of the valve and 
clearance taken from the face F, tends to hasten the mo- 
ment of closure in one stroke and delay it in the other, 
without producing the slightest effect on either the periods 
of cut-off or the extent of the lead, both of which are con- 
trolled solely by the outer edges of the valve face ; vice versa 
for a back-action engine. Hence, any valve that is found 
on examination to give unequal exhaust closure, clearly 
proves a great lack of appreciation on the part of its de- 
signer, of those simple means which lie at his disposal for 
the accomplishment of a perfectly correct exhaust and 
release. 

To illustrate this mode of equalization, 

Suppose that in the General Example of Part I, the 
crank and rod ratio was 1 : 4. 

Its mean exhaust-closure angle being 142, or a piston 
position of about 0.89 of the stroke, we have by the Stroke 
Table a difference angle of about 9 degrees. 

If then one-half of this difference angle, or 4J degrees, 
be laid off from the Base line on the 5|" travel line of the 
Scale (as in Fig. 12) we will obtain a correction of J inch, 
which added to the face N gives — 

N=2 T y + l n =2^ inches, and subtracted, 
F:=2 T y-J=2 1 inches. 

The true dimensions of the faces F and N, for imparting 
equalized exhaust closure with the given ratio of 1 : 4. 



EQUALIZATION OF THE CUT-OFF. 05 



EQUALIZATION OF THE CUT-OFF. 

Where an attempt is made to equalize the cut-off, that 
of the exhaust closure should be disregarded, for the only 
process that it is possible to adopt in such a case would 
practically achieve both results. 

Since the four periods, at which lead opening commences 
and cut-off occurs, are regulated by only two edges of one 
valve actuated by a single eccentric, it must be evident that 
where inequalities exist between any two of the four angu- 
lar positions of the eccentric, their mutual dependence will 
be such that the periods for these can only be equalized at 
the expense of the other two. 

Hence the equalization of the cut-off depends entirely on 
the expediency of giving a greater amount of lead to the 
one stroke of the piston than to the other stroke. With 
high-speed engines, such a change cannot be considered as 
desirable, but with those of low speed it may be made with 
very beneficial results. For with high speed the effect of 
lost motion can be most successfully overcome by a valve 
having equal lead in both strokes, but if the workmanship 
be perfect and the boxes carefully set up, the adjustment 
becomes applicable to all speeds. 

To equalize the cut-off* only two alterations are required 
in the valve motion, viz : 

1st. An increase of the angular advance. 
2d. A lengthening of the eccentric rod. 

To illustrate the process, suppose we were required to 
equalize the cut-off and exhaust closure of an engine, differ- 
ing only in respect to the connections, from that described 
in the General Example of Part I. 
5 



66 EQUALIZATION OF THE CUT-OFF. 

Let the ratio of crank to connecting rod=l : 5| and the 
forward stroke lead angle* =4°. 

From the Stroke Table we find that the return-stroke 
angle for the above crank and rod ratio with § cut-off = 
114°, or an angular advance for a valve without lead of 33°. 
With a lead angle of 4° the trial angular advance becomes 
=35° and the lap angle=31°. As the port opening equals 
1J inches, we readily find from the Travel Scale the follow- 
ing terms : 

Travel =5 J". Lap=l 1 V'. and forward lead= T 3 e inch, 
nearly. 

The difference between the forward and return-stroke 
crank angles for the above ratio and cut-off = 9 1°. One- 
half of this difference or 4|° forms the correction appropri- 
ate to the angular advance. Adding this quantity to the 
trial angular advance, we obtain 40° for the true angular 
advance of the eccentric. We thereby secure all the terms 
necessary for determining the length of the eccentric rod as 
already explained. 

With an angular advance of 40° and no irregularity in 
the piston motion, the exhaust would close in both strokes 
at a crank angle of 140°, or a piston position (Table A) of 
0.883 the entire stroke =26 J inches. The lengthening of the 
eccentric rod, however, corrects the irregularity produced 
by the connecting rod and preserves this same point of ex- 
haust closure to the motion. 

By measuring the distance between the true and trial 
angular advances— 40° and 35° — we obtain a distance T 3 e 
inch, by which it is necessary to increase the minimum 
width of the bridge B, making its new value =-§+ ye = \l 
inch. 

* Since from the nature of the case, the return-stroke lead angle must greatly 
exceed that of the forward stroke, the latter quantity should be taken at only 
3°, 4° or 5° to prevent the former becoming excessive. 



EXPERIMENTAL TEST. 67 

The lead angle of the return stroke will equal that of the 
forward stroke added to the difference between the cut-off 
angles of the crank, or 4° + 9|°=13| degrees. 

The lead opening of the return stroke, will equal twice 
the measured distance between the angular advances added 
to the forward lead, or T 3 / x2+ iV'= f$ inch. 

It should be observed that lengthening the eccentric rod 
increases the width of the return stroke port opening at the 
expense of that of the forward stroke, but so long as the 
width of the latter exceeds the minimum limit (page 23) for 
perfect admission, such inequality is actually a matter of 
not the slightest consequence. 

To guard against the danger of a contracted opening, it 
will be advisable when finding the travel for a corrected 
motion to estimate the width of the port opening at least 1 
or 11 times the width of the steam port. 



EXPERIMENTAL TEST. 

The greatest nicety and refinement of adjustment may 
be employed to produce an equal admission and exhaust 
of the steam throughout both strokes, and yet the attempt 
to equalize the power fail from lack of a judicious arrange- 
ment of the steam pipes and passages, on account of which 
the steam will enter one end of the cylinder with a lower 
average pressure than the other. This inequality occurs 
more frequently with vertical cylinders than horizontal 
ones, its extent can only be detected by the Engineer's 
most valuable friend, the Indicator, whose card ever fur- 
nishes clear and indubitable proof of the character, time 



68 EXPERIMENTAL TEST. 

and correlation of the various events taking place within 
the cylinder.* 

To illustrate the character of this inequality, a few 
cards are here inserted which were taken from a shop en- 
gine, having a vertical unjacketed cylinder. The engine has 
been in service for several years. Its steam pipe, supported 
by the roof girders, descends to the centre of the cylinder's 
length where it enters passages for conducting the steam 
to the upper and lower ports. From the nature of the case 
the passage to the lower port is more direct than that to the 
upper, hence the steam encounters less opposition and en- 
ters with a higher average pressure than through the other. 
The dimensions of the engine are the following : 

Diameter of cylinder =10&" ; Stroke=20f". 

Connecting rod =51 J" ; Ratio 1 : 5. 

Eccentric rod=62^". 

Travel of valve = 3 §" ; Lead = J inch. 

Steam ports =f"xlOJ" 

Outside lap=f" ; Inside =§". 

Average boiler pressure =65 lbs. ; Velocity =100 Eev. 



For the purpose of securing a well-defined card the 
boiler pressure was reduced to 42 lbs. per square inch, and 
the revolutions of the fly wheel — by means of a brake— to 
40 per minute. 

The result is given in Fig. 14, where the full line repre- 
sents the card of the forward stroke, the dotted that of the 
back. In making comparisons of this kind it should al- 

* For a complete analysis of this instrument, its practical operation, etc., the 
reader is referred to Mr. Charles T. Porter's Treatise on the Richard's Steam 
Indicator, enlarged by F. W. Bacon, M. E., and published by D. Van Nos- 
trand, New York. 



EXPERIMENTAL TEST 



60 



ways be borne in mind, that the steam line of the one card 
must be combined with the exhaust of the other before the 



Fig. 14 



Scale. 




true relation is expressed between pressure and resistance. 
The difference in the steam pressure for the two strokes 
amounted to about 2 lbs. The cut-off took place at — 

17 yV inches in the forward stroke 
15| " " return stroke. 

Difference^ l T 5 g inches. 



The compression commenced at 18|" forward. 
" " " • 17J return. 

Difference = 1 inch. 

This case is that of a valve motion in which no attempt 
has been made to equalize either the points of cut-off or 
exhaust closure. Had the exhaust closure been equalized 
the lines ab, c d, would have coincided. 

Subsequently, the equalization of the cut-off and ex- 
haust closure was accomplished with the same valve, by 
increasing its angular advance 5° and extending its eccen- 
tric rod. 

The effect of these changes is shown in Fig. 15 ;* both 

* The angles are constructed on the supposition that the piston is connected 
with the crank by means of a slotted cross-head and rod. The true angles of 



70 



EXPERIMENTAL TESTS. 



Fig. 15. 



Mldbs. 




cut-offs took place at 15| inches, compressions at 17| 
(return stroke locations), the lead angle of the forward 
stroke became 4§° and that of the return 14|, corresponding 
with an \ inch lead forward and an \ inch "back. 

the crank, however, for any ratio of crank to connecting rod, may readily be 
determined from these by first finding the piston positions due to these angles 
in Table A and then searching the Stroke Table for the forward and back 
stroke angles, appropriate to such positions. 



TO SET A SLIDE VALVE, 



71 



It should be observed that this great inequality in the 
lead, so long as the port opening was ample, produced but 
trifling effect on the area enclosed by the card. 

The two cards of Fig. 15 have been combined to form 
Fig. 16, showing an equality of the cut-off, exhaust closure 

Fig. 16. 





$c 


ale 

1 — totts 




RETURN- : ~ 


.35 




FORWARD 


SO 
_2tf 
—10 


AIR IMF \ 


_J 






and release, but the same excess of pressure as before on 
the return stroke. Had the cylinder lain in a horizontal 
position, the latter inequality would have entirely disap- 
peared, and equalized power been applied to both strokes of 
the piston. 



HOW TO SET A SLIDE TALTE 

HAVING EQUALIZED EXHAUST. 



1st. Place the crank at the 180° location, mark on the 
cross-head and one of its guides opposing " centre punch " 
points. 

2d. Bring the crank to the zero and mark a second point 
on the guide. The two points thus found, measure the 
length of the stroke. Move the eccentric until the valve 
has the required lead for the forward stroke. 

3d. Advance the crank in the direction of the motion 



72 TO SET A SLIDE VALVE. 

until the exhaust of the opposite stroke closes ; scribe a 
line across the guide which shall pass through the point on 
the cross-head. 

4th. Move the crank until the other exhaust closes and 
scribe a second line on the guide. 

5th. If now the exhaust should close at equal distances 
from the commencement of each stroke the motion would 
be in adjustment ; if not, alter the length of the eccentric 
rod until the closure becomes equalized, then return the 
crank to the zero position, and alter the angular advance of 
the eccentric until the required lead of the forward stroke 
is secured. 



The position of the valve at the moment of closure may 
readily be fixed by means of a " valve gauge" fitting centre 
punch points on the valve stem and its stuffing box. 

The above process will serve also to equalize the cut-off 
if the valve be proportioned for this object. 



PART III. 



ADJUSTABLE ECCENTRICS. 



ADJUSTABLE ECCENTRICS 



The intensity of the resistances, opposed to the action of 
steam npon the piston of an engine, fluctuates in a very- 
marked manner, and were it possible to meet variations 
instantaneously "by an increase or diminution of the power 
applied, the result would be an impulsive action of the 
working parts instead of a smooth continuous motion. 

It is obvious then that the power of an engine must 
be exerted at different periods of time in overcoming a more 
and more determined resistance or even one acting in an 
opposite direction. 

Slight variations in the resistances are controlled or 
absorbed by the momentum of the working parts, as by the 
fly wheel of a stationary engine, the drivers and coupled 
wheels of a locomotive, and the screw or paddle wheel of a 
steamer. 

But variations in degree must be met by an increase or 
diminution of the power applied. This may be accom- 
plished in two ways, either by controlling the pressure of 
the steam before it enters the cylinder or by limiting it after 
an entrance has been effected, that is by cutting off at an 
earlier or later point of the piston' s stroke. The first method 



76 ADJUSTABLE ECCENTEICS. 

deals with the throttle valve, the second relates to the clos- 
ing of the steam port by its valve, while for marine pur- 
poses both of these agencies are usually employed. 

The throttle may be operated either by hand or by an 
automatic device called a ''governor," the principle of which 
has been so clearly elucidated in almost every work on the 
Steam Engine that it would appear superfluous to repeat it 
in this connection. The governor is also at times used as a 
regulator of the cut-off, a work it most beautifully and 
delicately executes in such stationary engines as the " Cor- 
liss," " Allan," and others. In these the steam and exhaust 
ports are perfectly distinct, so that a change in the cut-off 
does not affect the action of the exhaust, which remains from 
the beginning to the end of the stroke free of the back 
pressure peculiar to a single eccentric motion. 

The principal regulator of the cut-off in modern practice, 
however, is the "link," or combined double eccentric mo- 
tion, which retains, while presenting itself in various kindred 
forms, the individuality of the double eccentric. On 
this account the study of the action of an adjustable single 
eccentric forms the best introduction to a complete under- 
standing of the link motion. 

Hitherto we have considered the eccentric as a fixed 
body keyed to the main shaft, with its centre line or throw 
inclined at a certain angle to the crank arm. Thus in Fig. 
17 the eccentric has an angular advance of 33 J° or a position 
C F, suitable for a positive or forward motion of the crank 
if a rocker intervenes between the eccentric and the valve. 
It will be remembered (Fig. 9) that the same eccentric, when 
located with an opposite angular advance C B, holds a 
position appropriate to a negative or back motion of the 
crank. Hence if it be required to change the direction of 
the engine's motion, it is only necessary to unkey the 



ADJUSTABLE ECCENTRICS 



77 



eccentric, slip it around the shaft and secure its throw in a 
position C B, opposite to that of C F. 

But if in addition to a change of direction a variation in 
the cut-off for the forward and back motions of the crank 
were demanded, subject to the single condition that the lead 
opening and lap shall remain unaltered, then it would be 
very clear that the eccentric must be slotted in such a 
manner that its centre can pass in a direct line from F to B 
(Fig. 17) instead of following the arc F m B. By this 

Fig. 17. 




means the throw of the eccentric and consequently the 
travel of the valve would be reduced between F, the full 
gear forward of the eccentric, and B the full gear back, while 
the minumum value would lie at the point M midway 
between these extremes, or at the mid gear of the eccentric. 
When the eccentric is placed at / 2 , the \ travel of the valve 
equals cf 2 ; at f z —cf z and at the mid gear=C M. It 
need scarcely be told one already familiar with the use of 



78 



ADJUSTABLE ECCENTRICS 



the Travel Scale, that by thus reducing the travel of the 
valve — while the lap and lead opening are preserved con- 
stant — we obtain a reduced port opening, an increased 
angular advance, and consequently an earlier cut-off. Be- 
fore proceeding, however, to analyze the effects of these 
changes one other case should be considered, namely that in 
which the lead opening admits of slight variation . The most 
common form in which this occurs is for the lead opening to 
increase from the full gears towards the mid gear as in 
Fig. 18, where the centre of the eccentric travels in an arc. 

Fig. 18. 




• The reverse, or case of diminution, is so similar in prin- 
ciple, that the examination of one will serve to indicate the 
nature of the other. 

Suppose, for example, that C F, the full gear throw of 

the eccentric — 2^ inches. 

Then the greatest travel of valve =5 " 

Let the lap. =1 " 

And lead opening = f " 



ADJUSTABLE ECCENTEICS. 79 

These dimensions are chosen on account of no peculiar 
fitness in their relation to one another, but merely to illus- 
trate the effect of reduced travel, constant lap, and a varia- 
ble or constant lead upon the cut-off, lead angle, port open- 
ing and exhaust closure of a simple slide valve. 

With a Constant Lead opening the centre of the eccen- 
tric should be moved in a direct line from F to B, Fig. 17. 
When located at F, the travel of the valve equals twice 
C F=5 inches, the lap— 1", and lead=f" ; if now we mark 
the lap and lead on a slip of paper and apply it in the usual 
manner to the 5 inches line of the Travel Scale, we lind that 

The cut-off = 123° =0.77 stroke. 

The lead angle =10 degrees. 

The port opening =1J inches. 

The exhaust closure =14,6£°= 0.92 stroke. 

Upon removing the centre of the eccentric from F to/' 
the travel will be reduced to twice C F 2 =4". Lap and lead 
opening remaining unchanged, we find by applying them 
to the 4" line of the Travel Scale that — 

The cut-off=106°=0.64 stroke. 

The lead angle =14 degrees. 

The port opening =1 inch. 

The exhaust closure =136° =0.86 stroke. 

Since b* is removed the same distance from B that / is 
from F, the two positions/ 2 and & 2 will give precisely the 
same results for opposite motions of the crank. 

In like manner the cut-off, etc., for the positions/', b% 
and M may be readily found, but their mutual relation can 
best be exhibited by grouping their results in a Table like 
the following for — 



80 



ADJUSTABLE ECCENTEICS. 



Constant Lead. 



Eccentric 
location. 


> 


ci, 


6£ 

.s 

1 



-a 

h4 


Cut-off. 


►J 


ft 
O 

O 

P4 


~3 > 


Exhaust Closure. 


F or B 

foxF 

f a orb* 

M 


deg. 

5 
4 
3 

2| 


deg. 
I 

I 
I 

I 


ins. 
3 
8 
3 
8 
3 
8 
3 
8 


deg. 

123 =0.77 stroke. 
106 =0.64 " 

43^ = 0.14 " 


deg. 
IO 

14 

25 

43 2 


deg. 

Io 

I 

I 

3 

8 


deg. 

33i 
44 

67 
90 


deg. 

146.1 = 0.92 stroke. 
i 3 6~ = o.86 
113 =0.695 " 
90 =1 



Again, with Variable Lead opening, diminishing from 
the mid gear toward the full gears (from |" to J") the centre 
of the eccentric must move in the arc of a circle, as shown 
in Fig. 18, where the points/ 2 ,/ 3 are drawn a little nearer 
toward the centre of the shaft, thereby reducing the travel 
of the valve. A Table similar to the above has been con- 
structed for showing the effect on the motion of — 



Variable Lead. 



Eccentric 
locations. 



F or B 

/* or b* 

f* or P 

M 



deg. 
5 

3* 



ins. 
i. 
8 
J.J.-1- 
4 ' 3 2 

a. 



Cut-off 



deg. 

129^=0.82 stroke 
107 =0.65 " 

71 =i * " 
43^ = 0.14 " 





£? 




<sS 




3 


W> 


3 




B 


& 


rt c 


-0 




M> 








deg. 


Ah 


<; 


deg. 


deg. 


if 


«+ 


27 


IO* 


IS 

1 6 


44 


24 


A+& 


66|r 


43* 


3. 

8 


90 



Exhaust Closure. 



deg. 
153 =0.945 stroke, 

138* = * 
H3|=o.7 " 

90 =* 



From a comparison of the foregoing tables we are ena- 
bled to draw the following general conclusions : 

I. That whether the eccentric centre be moved along a 
straight line, or upon an arc, the cut-off and exhaust clo- 
sure will take place the earlier, the nearer its approach to 
the mid gear ; while the lead angle and angular advance of 
the eccentric will be increased in magnitude. 



ADJUSTABLE ECCEi\TEICS. 81 

II. At the mid gear — 

The port opening = the lead opening of the valve. 
Cut-off angle = lead angle of the valve. 
Angular advance =90°. 
Hence the exhaust closes at the J stroke. 

III. If the port opening =0, in the mid gear, then the lead 
opening =0, and the lead angle =90°. The steam conse- 
quently is not admitted to the cylinder for either stroke of 
the piston. 

IV. Since the free admission of the steam depends di- 
rectly on the area of the port opening, and this is gradually 
reduced towards the mid gear, it must be evident that the 
most influential element upon the perfect action of a link 
motion, or adjustable eccentric, will be this width of lead 
opening in the mid gear ; at which location it invariably 
equals the port opening. 

V. Whether the lead opening remains constant or va- 
ries from the full to the mid gear, the lead angle — or angu- 
lar distance of the crank from the nearest centre at the mo- 
ment the port commences to open for the admission of 
steam — increases in magnitude from the full to the mid 
gear. At this point, if the lead opening =0, the angular 
distance becomes =90°. This condition is of course incom- 
patible with motion, for the port opening being 0, no steam 
can enter to urge forward the piston, but could this be 
moved to the 90° or ^-stroke point by extraneous force, it 
would then be repelled by the steam admitted for the sup- 
ply of the return stroke. 

VI. To estimate, therefore, the effect of any lead on the 
continuity of the crank motion, it is necessary to know not 
only the width of the lead opening (or lead) at the end of 
the stroke, but also the angular distance of the crank (or 
lead angle) at the moment lead commenced. In other 

6 



82 ADJUSTABLE ECCENTRICS. 

words, we must know the area of the opening and the time 
required to produce it. Thus with a constant lead of | inch 
the port commenced opening for the full gear when the 
crank was within 10° of the end of the stroke, but for the 
mid gear when the crank was within 43J° of the same posi- 
tion, a portion of time nearly 4J times greater for the same 
opening. Since the volume of steam admitted through a 
contracted passage, depends more directly upon the time 
that passage is kept open than upon its area, it manifestly 
would be absurd to imagine that a valve motion, having 
constant lead, was capable of admitting steam with invari- 
able effect for all points between the full and mid gears. 
So far as preadmission alone is concerned, the lead opening 
should grow smaller on the approach towards the mid gear. 



The relations between travel, lap, lead and port open- 
ing for the different positions ¥,/%/% M, b% b% B of the 
eccentric, are conveniently expressed by a single diagram 
like Fig. 19. 

Describe the travel circle a' F B, lay off on both sides 
of the centre or exhaust-closure line c' C, the lap and lead, 
and draw the cut-off and lead lines. Through the various 
positions F,/ 2 , etc., draw indefinite lines parallel to the 
central line of motion a) d\ and upon these lay off on each 
side of the exhaust-closure line the ^ travel for the location 
in question. Thus, from d lay off c ] d and d a each equal 
to C F the I travel ; from c% c* h and & e each equal to 
C/ a , and so on. Finally, draw the curved lines d M d% 
a M 2 a 2 through the extremities of the travels for their boun- 
dary lines,* and we obtain a sort of travel scale expressive 

* The resulting curves will invariably constitute the branches of an equilat- 
eral hyperbola. 



ADJUSTABLE ECCENTRICS. 



83 



of "the character of the motion at the different gears of the 
eccentric. 

Fig. 19. 
TRAVEL 




Since for any particular case the lap absorbs a constant 
portion of the travel, as the distance I Z', it is evident that 
in order to obtain a variable cut-off, we hare sacrificed port 
opening and consequently the travel in both strokes, and 
have reduced its excess F d or B d 2 over the lead in the full 
gears, to nothing in the mid gear. This Figure will enable 
us hereafter to trace the analogy between link and adjusta- 
ble eccentric motions. 

Having explained the effects attending a motion of the 
eccentric's centre across its shaft, it is proper to indicate 
how such motion can be secured. 



84 ADJUSTABLE ECCENTEICS. 

The devices are naturally grouped under two clashes : 
1st. Those capable of acting upon the eccentric while 
the engine is in motion. 

2d. Those that require a state of rest for their manipu- 
lation. 



The idea of moving the centre of an eccentric directly 
across its shaft, by means of two wedges with reversed 
points, first originated with Mr. Dodd, of Newcastle, Eng- 
land, and a device similar to that shown in Figure 20 was 
patented by him in 1839. His object was simply to obtain 
a reversable valve motion, little dreaming at the time of its 
latent powers as a variable cut-off. These were subse- 
quently developed by Mr. Dubs of Glasgow and success- 
fully applied, with slight modifications of design, to many 
locomotives. 

In the accompanying figure the crank A is placed at the 
zero, as well as at right angles to its mate G. The valve 
motion of its cylinder is operated by the eccentric pulley 
D, whose centre f 2 may be moved across the shaft to any 
other position between F and B, by withdrawing or insert- 
ing the wedges d d secured on one side of the sliding pulley 
H. In its opposite side are two similar wedges e e, for oper- 
ating the pulley E, which controls the valve of the cylinder 
belonging to the crank G, and consequently moves in a line 
n n 2 at right angles to F B. If now the pulley II be slid 
along the crank shaft until brought in contact with the 
eccentric D, the centre/ 2 will be transferred from/ 2 to 
B, and in like manner n ] to n 2 , locations appropriate to a 
back or negative motion of the crank. When however it 
comes in contact with the eccentric E, the two eccentrics will 
stand in the full gear forward positions F and n, and the 
nearer the pulley H approaches the mid position between 



ADJUSTABLE ECCENTIIICS. 



85 



D and E tlie earlier will tlie cut-off take place, as already 
shown in Fig. 17. 

A moment's reflection will satisfy the mind, that the 
Dodd Wedge Motion cannot be corrected for inequalities 
of cut-off and exhaust closure due to angularity of the 
connecting rod, without introducing mid gear inequal- 
ities of port opening, far more pernicious in their effects 
than the evils we seek to abate. 

The second class of motors find their chief application in 
connection with portable engines where it is seldom neces- 
ary to reverse the direction of the crank motion. The 
mechanical arrangement of the parts is shown in Fig. 21. 

Fig. 21. 




The collar H, being firmly keyed upon the main shaft c g, 
carries on one side a bolt A which performs the office of a 
pivot to the slotted eccentric pulley E. Through the oppo- 



86 ADJUSTABLE ECCENTRICS. 

site side passes the bolt D fitting loosely the slot D d and 
capable of clamping the pulley in any desired position. 
The eccentric has an angular advance of 30° and its centre 
occupies the full gear forward position F. To place it in the 
full gear back position at B, the bolt D should be loosened 
and the pulley E turned on its pivot A until the point d 
assumes the position D. This motion will transfer the cen- 
tre F, upon an arc whose radius equals A F, across the 
shaft to B, and give as in Fig. 18 an increasing lead from the 
full to the mid gear. If however it were required that the 
lead be preserved constant for all gears of the eccentric, the 
curvature of the slot D d should be formed with a shorter 
radius than D A, a similar change should be made in the 
large slot, and the hole for the bolt A should be oval in the 
direction of the line A F so that the pin B might force the 
centre of the eccentric to adhere practically to the straight 
line joining F and B. 

Figure 21 illustrates a simple method for determining 
the diameter of the eccentric pulley and for arranging the 
centres in such a manner that the large slot shall be dis- 
posed symmetrically on opposite sides of the diameter A 
F. The process is carried out as follows : 

1st. About the centre C describe a circle c g, with a 
diameter equal to that of the proposed shaft. 

2d. Decide upon a suitable diameter for the eccentric 
pivot A and locate the bolt as near to the shaft c #, on the 
central line of motion, as consistent with the strength of 
the pulley. 

3d. With A as a centre and A C radius describe an arc 
C c ; join A with its point of intersection c of the shaft circle. 

Bisect the angle C A c by the line A F. 

4th. Lay off the required angular advance line C F. Its 
intersection with the line A F locates the centre of the eccen- 



ADJUSTABLE ECCEXTKICS 



87 



trie in the fall gear forward. About F as a centre strike a 
circle for the eccentric enclosing the pin A by a distance 
sufficient to give ample strength to the eccentric pulley. 
The distance C F will then equal the J travel of the valve, 
with which radius the travel circle F B may be described, 
and the lap readily determined. 



The angular advance is usually taken at about 30° or 
the | cut-off, but of course the larger the advance the 
greater will be the travel of the valve, lap, &c 




lh3 above cut illustrates another modification of the 
adjustable eccentric. In this device, the collar H is made 
larger than the eccentric pulley, and keyed fast to the 
shaft. The pulley E is secured by the bolt A, and any 
tendency to its rotation prevented by means of a feather on 
the back, which fits the slot d. 



PART IV. 



LINK MOTIONS 



LINK MOTION 



The various mechanical devices embraced under this 
general term, have many strong points of resemblance and 
subserve a common object. By means of them, the Engi- 
neer is able at will to change the direction of the crank ro- 
tation, with only the loss of the time required for overcom- 
ing the momentum of the moving parts, and developing the 
like in a reverse direction. More than this simple result 
was not contemplated in the original discovery of the link. 
Subsequently, however, it was found to be capable of regu- 
lating the cut-off of the steam, so that the power could 
always be adjusted to the work required. This feature 
greatly enhanced its value, and placed the engine under the 
complete control of the operator. 

The extreme simplicity of the parts of the link motion, 
has enabled it to contend successfully with all rivals, and 
at the present day it remains in substantially its primitive 
form. It is applied principally to locomotive and marine 
engines, where the power demanded is quite variable, and 
the motion at one time direct, at another reverse. 

The designs may be divided into four classes : 

I. The shifting link motion. 

II. The stationary link motion. 

III. The Allan link motion. 

IY. The Walschaert link motion. 



92 SHIFTING LINK MOTIONS. 

The first form was invented by Mr. Howe, in 1843, and 
applied to the locomotives of Messrs. Robert Stephenson & 
Co. It is in fact the representative link motion, which, ex- 
cepting slight modifications in the mode of suspension, 
remains unchanged by the accumulated experience of a 
quarter of a century. 

Simultaneous with the appearance of this motion was 
that of the second, the discovery of Mr. Daniel Gooch. It 
accomplishes perfectly analogous results, and has met with 
much favor throughout Great Britain and the Continent. 

The " Allan" combines the characteristic features of the 
Howe and Gooch link motions in such a manner that the 
parts are more perfectly balanced, consequently it dis- 
penses with the counter weight or spring peculiar to the 
former of these motions. 

The Walschaert motion is extensively applied in Bel- 
gium, but probably will not receive much attention from 
locomotive Engineers, beyond the limits of that Kingdom, 
unless future designers succeed in reducing the number of 
its connections. 

It is proposed to confine our investigation to the shifting 
link motion, to develop the general laws governing its ac- 
tion amid varied conditions, to present graphic methods for 
determining the proportions of the parts, and briefly to 
point out the general application of the same to the link 
motions of the other three Classes. 



SHIFTING LINK MOTIONS. 

A link, operated by two fixed eccentrics, forms when 
properly suspended an exact mechanical equivalent of the 
movable eccentric. Unlike the latter, however, its motion is 



SHIFTING LINK MOTIONS. 98 

capable of an accurate adjustment, which practically nulli- 
fies the effect of irregularities in cut-off and exhaust closure, 
attributable to the angularity of the main connecting rod. 

The general form in which its parts are arranged in 
American locomotive practice, is clearly shown in Fig. 22. 
Upon the main shaft are keyed the forward and backing 
eccentrics, with their centres at F and B, the two extreme 
positions of the single movable eccentric in Fig. 17. Their 
straps are bolted to the eccentric rods, and these in turn 
are pinned to the "link." The slide valve is attached by 
its stem 'to one of the rocker arms, and a "block" sur- 
rounds the pin of the opposite arm, which fits the main 
link and slides . freely therein. The centre of the link is 
spanned by a plate called the " saddle," on which is formed 
the pin or stud that supports the link and eccentric rods. 
This pin is embraced by a bar called the "hanger," or 
sometimes the suspending or the sustaining link, from its 
position and the service rendered to the motion. The 
former term is preferable on account of its conciseness, and 
can lead to no confusion. The opposite extremity of the 
hanger is attached to one arm of the tumbling shaft. Both 
arms of this shaft are rigidly secured, and form upon it a 
"bell crank." The shaft itself freely oscillates on prop- 
erly supported bearings, but is limited in its motion by the 
action of the reversing rod. The link has been dropped 
into the full gear forward, thus throwing the entire influ- 
ence of the eccentric F upon the valve motion to the almost 
complete exclusion of that of its mate B. By drawing back 
the reversing rod and raising the link until the pin of the 
other eccentric rod is brought in line with the pin of the 
rocker arm, the link will be made to occupy a location ap- 
propriate to a negative crank movement (as with B, Fig. 17) 
and intermediate suspensions will in like manner be pro- 



94 SHIFTING LINK MOTIONS. 

duetive of earlier cut-off and exhaust closures. In order to 
clearly demonstrate that such similarity exists between 
these motions, it will he necessary to reduce Fig. 22 to a 
skeleton form like Fig. 23, and follow the journeyings of 
the "link arc" throughout a complete revolution of the 
crank. 

Let the path of the main crank pin he represented by 
the circle E D in Fig. 23. This being divided into 12 equal 
parts, gives a sufficient number of positions for the purpose 
of tracing the motions of the link arc. The zero will be 
known as position No. 1, the 180° as position No. 7, and so 
on. Within this circle describe the path of the eccentric 
centres by means of the circle F B b\ This should first be 
divided into 12 equal parts, with F as the origin of one ec- 
centric' s motion, and again into 12 other equal parts with 
B as an origin, so that when the crank moves from position 
No. 1 to 3 the new positions /' and b 3 of the two eccentrics 
may be instantly found, and the same with other locations. 
The original positions F and B are of course laid off with 
the angular advance due to the proposed maximum cut-off. 
At the distance C t from the centre of the shaft erect the 
perpendicular T t and locate T the fixed centre of the tum- 
bling shaft. T h will represent the arm which supports the 
link through its hanger and Ji 7i' 7i" the arc described by 
this arm. A second perpendicular at the distance C A will 
contain the point K, the centre of the rocker shaft, whose 
arm R A sweeps the arc r A r. The motion of the upper 
arm, being merely the reverse of the lower, need not be 
considered, and so long as the angular advance is properly 
located no error can arise from the omission. In the mo- 
tion of the lower arm there are five locations of vital im- 
portance, viz : one at which the exhaust of the valve opens 
or closes, two appropr'ate to the lead at full gear of the 



SIIIFTIXG LINK MOTIONS. 95 

link, and two at wliicli cut-off takes place or the valve 
closes its ports. The 1st is evidently the normal position 
,R A of the rocker, the 2d ~R d, R d\ that in which the 
rocker pin is drawn aside a distance A d equal to the sum 
of the lap and lead, and the 3d R 7, H V corresponds with 
a removal A I equal to the lap. Hence, so far as the slide 
valve is concerned we can confine our attention to the mo- 
tion of the rocker arm pin upon the arc r r. The five posi- 
tions in question can he distinctly located hy sweeping a 
circle d d\ with a radius equal to the lap plus the lead of 
the valve, around the exhaust point A, and inscribing a 
second circle I V with a radius equal to the lap of the valve. 
Then the four points in which these circles intersect the arc 
r r will give the 4 positions of the pin corresponding with 
the lead and cut-off positions of the valve, and the centre 
of these circles will give the exhaust closure positions. As 
these locations will he constantly referred to in the sequel, 
it should he remembered that the "lead circle" d d' lixes 
those points on the arc r r which the pin of the rocker arm 
must occupy when the valve has a given lead ; and that 
the "lap circle" I V locates the positions of the same pin 
for the moments at which the steam ports are closed against 
the admission of steam to the cylinder. 

Our next duty will be to reduce the link to its simplest 
form. 

It appears on examination that the rocker pin is entirely 
subject, in its motion, to the guidance of the link arc, and 
that this arc swept with a radius C A is rigidly connected 
with three moving points, viz. the saddle pin, and the two 
eccentric rod pins. In following the motion of the link arc, 
the connection of the parts can best be maintained by the 
use of a template, cut from white holly veneer or other 
hard wood and shaped like L L in Fig. 23, upon which are 



98 SHIFTING LINK MOTIONS. 

made V shaped incisions for locating the points /, S and b 
of the pins. 

We are now prepared to find position No. 1 of the link 
corresponding with No. 1 of the crank. Of course when 
the crank is at the zero the steam port should be opened an 
amount equal to the lead of the valve. The rocker arm 
therefore will occupy the position H d, and the point d lie 
in the link arc. Since the eccentric centres F, B are found 
in a line perpendicular to the central line of motion, and 
the eccentric rods are of equal length, the link must occupy 
a nearly perpendicular position. Place the template so that 
its arc coincides with the point d and mark the point /upon 
the paper, then the distance from F to f will equal the 
length of the eccentric rod. With this length as a radius 
describe about F as a centre the small arc / g, likewise 
with B as a centre describe the small arc b h. Apply the 
template to these arcs so that the points f and b shall be 
found in them and the point d on the link arc n c d, after 
which, draw the link arc- on the paper and we obtain posi- 
tion No. 1 of the link. With the saddle pin S as a centre 
and the length of the hanger 7i S as a radius, the position T 
7i of the tumbling shaft arm is readily found for full gear 
of the link and conversely the arc c S c is fixed along which 
the saddle pin must travel during the revolution of the 
crank. 

The preparatory stages of our solution are now complete, 
the link motion of Fig. 22 has been reduced to its skeleton 
form and the first position of the link located. Our next 
step is to follow the link arc during its journeyings in a 
single revolution of the crank. Suppose then, the crank 
is made to occupy position No. 2, the eccentrics will be 
carried forward from F and B to/ 2 b 2 . Since the length 
of their rods remains unchanged the arcs / ' g>b ft, will be 




yr Shaft 



Central Line ofAfotion 






IM 




y> 








A-i / .y 


„.^„ 


*L_ 






/ 




SHIFTING LINK MOTIONS. 
Fig. 24. 



97 



P/N.f. 

CENTRAL LINE OF MOTION 



7 
-• 

PIN.h. 




removed from their first position and the link template will 
follow them with its points b and /. The only restraint 

7 



98 SHITTING LINK MOTIONS. 

upon the course of this template is that the point S must 
travel on the hanger aro c c. If therefore we describe new 
arcs about the centres/? & 2 , and adjust the template so that 
f and b shall be found in those arcs and S in the arc c c 
there will result a new link position with its arc standing 
like 2 2 in Fig. 24 and intersecting the rocker pin arc r r at 
a point Jc. But as the rocker pin necessarily follows the 
course of the link arc it will by this change be drawn aside 
from d to k, consequently the steam port will be opened 
wider by the extent of the horizontal measurement of this 
distance. In like manner when the crank is carried to 
position No. 3 the link arc will be removed to 3 3 as in 
Fig. 24, and the rocker pin to V, producing thereby a still 
wider opening of the steam port. The same process applied 
to the remainder of the 12 crank positions will give the 
other locations of the link arc (as in Fig. 24) for the full 
gear of the link. Now observe that the link position 3 3 pro- 
duces the widest opening of the steam port, and as the crank 
advances to 4 and 5 this opening grows less and less, until 
between 5 and 6 the rocker pin reaches the point I, where the 
steam is finally cut off. During its further progress expan- 
sion goes on and at last when A is attained the exhaust 
opens and the steam escapes. At position No. 7 (the 180° 
location of the crank) the link arc is brought again in con- 
tact with the lead circle and a like process is repeated 
throughout the return stroke. 

A duplicate set of link arc locations, might readily be 
obtained by raising the link to the full gear back position 
and a similar set for the mid gear, but an examin- 
ation of the one just found will develop the character 
of the motion. Draw curved lines* tangent to the 

* Hyperbolic curves with semi-transverse axes shorter than their semi -con- 
jugates. 



SHIFTED LINK MOTIONS. 



99 



extreme positions of the link arc to represent the boun- 
day lines of the valve travel, as B B' B" and D D" in 
Fig. 25. From the centre of the main shaft, with a ra- 



Fig. 25. 




— 75 



n-/oo 



dius equal to C A sweep an indefinite arc A A' A" for the 
exhaust-closure line, and parallel arcs I I' I" for the cut-off 
lines. Draw lines d D ? d n and d B' d n tangent to all the link 
arc positions No. 1 and No. 7 ; these show, by their distances 
from the cut-off lines, the variable character of the lead 
opening at the extremities of the stroke. 

Comparing Figures 25 and 19 we find that the shifting 



100 ADJUSTMENT OF LINK MOTIONS. 

link, with its two eccentrics, gives results precisely analo- 
gous to those of the adjustable eccentric, consequently all 
the inferences (page 81) we were able to draw from the lat- 
ter motion, will hold with equal force in the case of the 
former. 



ADJUSTMENT OF LINK MOTIONS. 

Besides the qualities possessed in common by the two 
motions, the link has that of adjustability, a very impor- 
tant feature, and one which specially characterizes it. As 
the tendency of the connecting rod angularity in a direct 
acting engine is to produce a later cut-off on the forward 
stroke than the amount required, and since with the link the 
cut-off in either stroke depends on its degree of elevation 
or depression ; it follows that if we suspend the link in 
such a manner as to cause a suitable elevation for the for- 
ward stroke, the result will be a perfectly equalized motion 
for the gear in question. And again if the equalization 
be made applicable to all gears, then the link may be 
suspended at any point between the full forward and 
full back without an appreciable inequality appearing 
between the cut-offs or the exhaust closures of either stroke. 

But a practical difficulty here arises ; the link block 
moves upon a fixed arc r r while the link rises and falls, 
consequently for each revolution of the crank the link will 
slip back and forth a certain distance on its block. Should 
this slip be excessive in any particular gear and the engine 
run a long time in this gear, the faces of the Jink would 
become worn, "lost motion" would ensue and the delicate 
action of the parts would be destroyed. 

Hence in planning a serviceable link motion it is neces- 



CONNECTION OF ECCENTRIC EODS. 101 

sary to reduce the slip of the link to its smallest value, con- 
sistent with the equalization of the motion, and in marine 
engines to even sacrifice the equality of the cut-offs to the 
reduction of the slip. In Fig. 24 the motion of the two 
fixed points (m and n) on the link have been traced in 
looped curves. The upper of these, shows to what extent 
the point m falls below and rises above the arc r r, giving 
a slip equal to the distance S plus S'. 

It is important to observe that the magnitude of the slip 
grows smaller and smaller as the link block draws nearer 
to the point of suspension, because this fact indicates that 
the stud of the saddle should be placed — when a minimum 
value of the slip is required at a certain point of suspen- 
sion — as nearly over such point as possible. 



OONjSTEOTION" OF ECCENTEIC EODS. 

The variable character of the lead opening in a shifting 
link motion depends upon the manner in which, its eccen- 
tric rods are attached, and its magnitude depends on the 
length of those rods. The force of this remark will appear 
from an examination of Figures 26 and 27. In both 
instances, the eccentric centres lie between the centre of the 
shaft and the link, while the latter for sake of simplicity 
has been made to act directly on the valve. The No. 1 
position represents the mid gear, and No. 2 the full gear 
forward of the link. If under these conditions the eccentric 
rods be crossed as in Fig. 26 the lead opening will decrease 
from the full to the mid gear of the link, where the motion 
may even be without lead. 

But with the open rods of Fig. 27 the lead opening 



102 CONNECTION OF ECCENTEIC RODS 

Fig. 26. 




Fig. 27. 




increases from the full to the mid gear, and the rapidity of 
this increase, for a given link, depends directly upon the 
length of the rods ; hence with a given mid gear lead open- 



CONNECTION OF ECCENTPJC RODS. 103 

ing that for the full gear will be determined mainly by this 
length. Excepting the case of valves having an independent 
cut-off (Part V.) the rods are seldom crossed as in Fig. 

26, yet (from conclusion VI, page 81) it is believed that 
many instances exist in which the arrangement might be 
adopted with good results. It is also possible, with such a 
motion, to stop the engine by placing the link in the mid 
gear ; but this can never be done with a motion like Fig. 

27, whose valve is invariably opened a certain amount in the 
mid gear. The extremes of mid gear lead opening in loco- 
motive practice are J and J an inch, but the more common 
value is f inch ; while the full gear lead varies between ^ 
and T 3 g inch, governed principally by the length of the ec- 
centric rods. 

With the stationary link the lead opening remains un- 
altered by changes in gear ; so that if § inch be assumed as 
the proper amount for the full gears, the motion will retain 
this lead for all gears between these extremes and the mid 
gear. This peculiarity is not inherent with the stationary 
link, since many shifting link motions may be arranged 
with a Constant Lead for the various gears of one direction 
of the motion. Take, for example, the motion shown in 
Fig. 22, in which the angular advance of each eccentric 
equals 21° and the lead enlarges from J" in the full, to f %" 
in the mid gear. By imparting an angular advance of 31° 
to the eccentric F, while that of B remains unaltered, the 
lead opening becomes constant for all points between the 
full gear forward and the mid gear, and diminishes from 
fe inch in the mid gear to J-" in the full gear back. Vice 
versa for a change in the angular advance of the eccentric B. 



104 CONNECTION OF ECCENTEIC EODS. 

PEACTICAL OBSEEV ATIONS. 

(based on fig. 22.) 

I. The tumbling shaft must be located at such a dis- 
tance above or below the central line of motion, that neither 
eccentric rod can strike against it when the link is moved 
from one full gear to the other. Special cases may arise 
that demand a curvature of the eccentric rod, but the prac- 
tice in general should be discountenanced. 

II. The hanger must be of such a length that the ex- 
tremity of the link will not conflict with the tumbling shaft 
arm in either forward or back gear. The length of the tum- 
bling shaft arm is usually equal to or greater than that of 
the hanger. 

III. If the link cannot be placed in full gear back, owing 
to the arrest of its tumbling shaft arm by the boiler or 
other opposing object, either the tumbling shaft must be 
removed and located below the link motion, or the rocker 
must be lengthened in order to depress the central line of 
motion and with it, the entire motion. When the latter ex- 
pedient is resorted to, a change should be made in the rela- 
tive positions of the rocker arms, for the purpose of pre- 
serving the identity of their motions. The proper inclina- 
tion W of the arms is found by describing a circle rttr (Fig. 
28) tangent to the central line of the valve stem, or a line 
sufficiently above the same to equalize the vibration of the 
stem, and the central line of the motion. Radial lines from 
the points of tangency will then give the relative positions 
of the arms. 

This method of correction is preferable to the former in 
respect to the symmetry of the motion, because the greater 
the length of the rocker arm, the less will be the vibration 
of the valve stem, as well as the slip of the link block. 



CONNECTION OF ECCENTEIC RODS. 10;") 
Fig. 28. 

v mm sim r. 



\* 




IV. So long as the angular advance of the eccentrics is 
laid off from a line at right angles to the central line of the 
link motion, the latter can be arranged at any inclination 
to the piston motion, without affecting the action of the link. 
These central lines were made to coincide in Fig. 22, merely 
for the purpose of simplifying the investigation, whereas 
they might have formed with each other any angle what- 
ever (see Fig. 52, Part V). 



106 GENERAL DIMENSIONS, 

GEIsTEEAL DIMENSIONS. 

In ordinary locomotive practice the dimensions of the 
various parts range between the following extremes : 

Ratio of crank arm to connecting rod 1 : 5-| and 1 : 8. 
Travel of valve 4 to 6 inches. 

Maximum cut-off from § to 0.92 of the stroke (gene- 
rally = 1). 

Mid-gear lead J" to §", usually the latter. 

Full gear (dependent on length of rods) ^g" to T 3 6 ". 

Radius of link 3' 6" to 6 ft. 

Distance between eccentric rod pins 10" to 14". 

Pins back of link arc 2\ to 3 inches. 

Saddle-stud back of arc 0" to 1J inches. 

Stud above central line of link 0" to 2F. 

Length of hanger 12 to 20 inches. 

Length of tumbling-shaft arm 14 to 22 inches. 

Length of rocker arm 8 to 11 inches. 



GENEEAL PEINOIPLES. 

OF THE GEOMETRIC SOLUTION. 

A cursory examination of the link motion might natu- 
rally lead to the conclusion— from the simplicity of the 
parts and the strong resemblance existing between their ac- 
tion and the single eccentric' s— that the theory of the latter 
being perfectly comprehended, but little difficulty would 
attend the work of assigning proper proportions to the 
former. Such an inference, however, would not be 



GEOMETRIC SOLUTION. 107 

strengthened by a closer inspection, much less sustained by 
an intelligent effort to accomplish a solution. The reason 
for this fact lies not only in the multiplicity of the parts, 
but also in the conflicting character of the elements that 
constitute a perfectly equalized link motion. 

The requirements of such a motion are—pe?fect equality 
of cut-off, of exhaust closure, lead opening and maximum 
port opening, together with absence of block slip, between 
the forward and return stroke of the piston for every sus- 
pension of the link from full gear forward to full gear back. 
Such theoretical excellence is absolutely impossible with 
the ordinary type of link motion, and efforts made to attain 
the same must necessarily result in failure. 

But good practical qualities may be obtained by sacri- 
ficing the non-essential to the essential points of the mo- 
tion. The action of the connecting rod on a link motion, 
may justly be compared to the distorting effect of pressure 
exerted upon one point of a symmetrical india-rubber ball, 
producing thereby a temporary concavity. This it is true 
can be removed by an even application of additional pres- 
sure to the adjoining parts, but the ultimate effect will be a 
bulging out of the central portion, and the symmetry can 
alone be restored by withdrawing all pressure. Just so 
with the link motion, the angularity of the rod tends to ren- 
der one or more events of the motion unequal in the oppo- 
site strokes of the piston, and should it appear more desira- 
ble to preserve certain ones of these than others, we must 
purchase their equality at the expense of the latter. Re- 
ducing the angularity of course diminishes its disturbing 
effect, hence in departments like locomotive engineering, 
where much attention is bestowed on the equalization of the 
motion, crank and connecting rod ratios of 1 : 7 or 8 obtain ; 
while in marine engineering ratios of 1 : 4 or 5 are common. 



108 GEOMETEIC SOLUTION. 

The subject of preserving the equalities of cut-off and 
exhaust closure at the expense of lead and port openings 
has been treated of in Part II. It will only be necessary to 
examine it here with reference to the mid gear. At this 
point the port and lead openings attain their minimum 
value, which being much less than the 0.6 or 0.9 port open- 
ing required for perfect admission, tends to reduce the pres- 
sure of the steam by wire-drawing, and if these openings 
vary, unequal powers will be applied in opposite strokes. 
Consequently the mid gear, lead and port openings must 
have equal values in both strokes, however irregular they 
may be in the full gears. No fixed limit can be assigned 
to the slip of the link on its block, but the amount allowa- 
ble under different conditions will readily be determined by 
the judgment of the Engineer. In every case, the main ob- 
ject is to reduce the slip to a minimum value for that gear 
in which the engine will be most frequently operated. 



GEOMETEIO SOLUTION 



LINK No. I. 



In designing an engine, as a 
general thing, no particular part 
can be isolated, its proportions 
assigned, and its details worked 
out regardless of the conditions 
inevitably imposed upon it by 
the character of the adjoining 
parts ; but rather, trial dimensions 
must be affixed, their adaptability 
tested and modified by circum- 
stances, and finally all must be 
unfolded and developed in per- 
fect harmony. When the sub- 
ject of scheming the link motion 
comes in order, we find that pe- 
culiarities of detail have already 

fixed the ratio of the crank arm to the connecting rod, 
have pointed out a convenient location for the rocker shaft 
and have more or less circumscribed the boundaries of the 
entire motion. 

Since methods of construction are always most intelli- 




110 LINK NO. I. 

gibly presented when the mind is able to follow their ope- 
ration in the solution of a practical -example, we will take 
for illustration of our method the following dimensions : 

Ratio of crank to connecting rod— 1 : 7J. 
Eccentric circle diameter =5 J inches. 
Maximum cut-off=0.92 stroke. 
Rocker from shaft =49 \ inches. 
c. to c. of eccentric pins =13 inches. 
Pins back of link arc =3 inches. 
Mid-gear lead=f inch. 

To find lap, full-gear lead, point of suspension of link 
and location of tumbling shaft. 



Spread upon a long drawing board, or table, two sheets 
of paper large enough to contain figures similar to 29 and 
31 when drawn on the Full Scale. The one will be used for 
locating the various important positions of the eccentric 
centres ; the other, for the journeyings of the link and its 
point of suspension, their centres should therefore be sepa- 
rated by the proposed distance between the shaft and 
rocker. 

Stretch a fine thread tightly across both papers in order 
to locate the right line E C D A, which constitutes, the 
Central line of Motion* 

Describe about the point C as a centre the eccentric 
circle EPD, with a radius equal to the throw of the eccen- 
tric. Then, with the points of intersection E and D as 
centres describe with an assumed radius equal arcs inter- 
secting at G and H and erect the perpendicular Gr C H to 
represent the neutral positions of the eccentrics. From this 

* The use of the T square should be avoided in all of the constructions. 



LINK NO. I. 



Ill 



line lay off an angular advance appropriate to the desired 
cut-off. Tins may be found in the subjoined Table : 



Cut-Off. 


Angular 
Advance. 


Return Stroke 
Maximum 

Cut-Off Angle. 


0.75 = l 

0.8 

O.84 

0.875=1 

0.9 
O.92 


28 degrees. 

25 " 
22 " 
20 " 
17 « 
16 " 


124 degrees. 
130 " 
136 " 
140 " 
146 " 
148 " 



In the present case the advance equals 16°, which laid 
off, by means of a protractor, from the line C G, determines 
the position F of the forward motion eccentric when the 
crank stands at the zero. In like manner B might be found, 
but it will always prove more convenient and accurate to 
take in a pair of dividers the distance between F and the 
point of intersection of the circle with the line G C and then 
prick off from the line G II the points b, f, B. We thus 
obtain the two positions F and B of the forward and back- 
ing eccentrics when the crank stands at the zero, as well as 
their new ones/ and b for the 180° location of the crank. 

It is well known that the inequality of the crank angles 
attains its maximum value at the \ stroke of the piston, 
hence the importance of examining the link motion with 
special reference to the \ stroke cut-off. Although appropriate 
angles for the crank have been furnished in the Stroke Tables 
it is thought best for facility of reference to here reproduce 
them in a more compact form. 



112 



LINK NO. I 





Crank Angles for 




Half- Stroke Position of ihe Piston. 


Ratio of 
Crank 








to Connecting Rod. 


Forward Stroke. 


Return Stroke. 




4 


82 1 degrees. 


97§ degrees. 




41 


»3i " 


964 " 




5 


84f " 


95l " 




5i 


84f " 


95s " 




6 


85 1 " 


94| " 




6i 


851 " 


94| " 




7 


85J " 


94g " 




7^ 


86| " 


93? " 




8 


86J " 


93i " 



If the ratio of crank to connecting rod be that of 1 : 1\ 
the two eccentrics will advance 86 J° from F and B while the 
piston travels to its forward \ stroke location, and 93 1° from 
/ and b for the return stroke. 

A very convenient way of locating these four points is to 
lay off from C F by means of a protractor, the point J / 
distant 86J , and f\ distant 93|° from /C. Then with 
a pair of dividers prick off these points at equal distances 
on the opposite side of E and D giving thereby the two 
other points \b and b\. In the nomenclature here adopted 
the letter f refers to that eccentric which produces a forward 
or positive motion of the crank, while b always designates 
the eccentric for the back or reverse motion. 

When a fraction is prefixed to either of these letters, it 
signifies some forward stroke position of the piston with the 
link in the forward gear, but if it follows the letter a return 
stroke of the piston with the link in the same gear. Thus, 
the \f represents the position of the forward eccentric when 
the link is in the forward gear and the piston has advanced 
to its forward \ stroke location, and f\ represents the same 
when the piston has attained its \ stroke return position. 
Having accurately located these eight important positions 



[ratio , l:7i .] 




''■"»"■ li,,, 



FIGURE 29 






( 'I'litr.i I Line of Mi 



FIGURE 30. 









Rocker Shaft 




> Foi'ward 



LINK NO. I. 113 

of the eccentrics, we pass to the other sheet of paper aud 
trace their influence on the proportions of the link attach- 
ments. 

Since the assumed distance of the rocker from the shaft 
is 49 1" and the eccentric rod pins are withdrawn 3" back of 
the link arc, the length of each rod will equal 49 \"— 3" =461''. 
Adjust a pair of beam compasses to strike arcs of 46 \ n 
radius. Step the needle point successively in the eight loca- 
tions of the eccentric's centres just found, and sweep from the 
central line of motion the same number of indefinite arcs (as 
shown in Fig. 30) upon which the eccentric rod pins must 
inevitably travel for the four given positions of the crank 
arm. 

Next, from a piece of white holly veneer cut a template L 
(Fig. 32) having a link arc of 49}" and with V incisions, 13" 
apart and 3" back of the arc to represent the location of the 
eccentric pins, and draw upon the same the three parallel 
lines f m,J S, b n ; making,/ S lie midway between/ and b 
as well as perpendicular to a line joining these points. We 
are now prepared to trace the journeyings of the link arc. 

I. To FIND THE MID-GEAR TRAVEL. 

For this purpose place the template in the mid gear 
positions No. 1 and 2 (Fig. 31) with its eccentric pins on the 
arcs F, B, /, b, and mark the points d), d 2 in which the link 
arcs intersect the central line of motion. Locate these 
points permanently by describing a circle through them, 
having its centre A in the central line. This point gives us 
the true location for the rocker shaft, the distance from the 
main shaft being equal to C A instead of 49}".* Through 
A, therefore, erect a perpendicular A R to the central line of 
motion and on it locate the centre R of the rocker shaft. 

♦ Their difference is always so trifling that the rocker box may readily 
be moved the proper amount and much difficulty of construction be thereby 
avoided. 



114 



LINK NO. I. 



II. To FIND THE LAP OF THE VALVE. 

From d) and d 2 lay off the mid-gear lead opening of f 
inch towards A, and permanently locate the positions thus 
found "by sweeping about the centre A a second circle I V. 
But since the mid-gear travel invariably equals the sum of 
the laps plus the mid-gear lead openings, the diameter of 
the circle I V will equal the sum of the laps, consequently 
the simple lap of the valve must equal its radius A I or A Z', 
Fig. 32. 

The following Table will aid the designer in the selec- 
tion of a suitable lead opening after the mid-gear travel has 
been determined. For since the value of the lead angle 
may range between about 30° and 40°, the widths of the 
openings will be those found in the Table. Of course much 
latitude is here allowed to the exercise of individual judg- 
ment, for the subject demands it. Observe, the larger trav- 
els are only found on marine engines : 



MID-GEAR DIMENSIONS. 



Mid-gear Travel. 


LEAD OPENING FOR A LEAD ANGLE OF 










30°. 


85°. 


£0°. 


i inch. 


1 inch. 


j\ inch. 


\ inch. 


iA " 


3 " 




5 it 


TS 


4 


T6 


2~ " 


1 tc 


3 tt 


7 it 


4 


8 


T6 


<■> 1 " 


5 tt 


7 tt 


9 it 


2 2 


T6 


T5 


1 6 


* " 


3 << 




1 1 it 


3 


8 


2 


T5 


3i " 


7 a 


5 tt 


1 3 it 


Iff 


8 


T6 


4 " 


1 tt 


1 1 tt 


1 5 ti 


2 


16 


1 6 



III. To FIND POSITION OF THE STUD FOE EQUAL CUT-OFFS 
AT THE ^ STEOKE OF THE PISTON. 

Place the template in position No. 3, with its eccentric 
pins on the forward ^-stroke elements \f\~b, and its link 
arc in contact with the lap or cut-off point I. Then mark 
upon the paper the position^' S occupied by its central line 



LINK NO. I. 115 

together with a portion of the link arc. Next, place the 
template in the position No. 4, with its pins on the arcs/ }, 
b J and link arc over the other cut-off point l\ after which 
mark on the paper the second position, / S', of the link cen- 
tre line. Having decided to suspend the link centrally, the 
point of suspension must he found on the line,/ S, and con- 
sidering the manner in which it hangs from the tumbling 
shaft it is evident that for a short distance the stud will 
practically move along some straight line c c parallel to the 
central line of motion. The point of suspension therefore 
must reside in the central lines j S, f S', must "be equally 
remote from the link arcs and at such a distance that a line 
drawn through the two points will prove parallel to the cen- 
tral line of motion. The only two positions satisfying such 
conditions are S and S', found by trial distances laid off 
with a pair of dividers from the two link arcs. Having se- 
cured the proper distance for the stud, fix it permanently, 
by making a V incision in the link template ; for as our 
subsequent study of the link will be intimately associated 
with the motion of this point, it is important to be able to 
mark its position for other gears of the link. 

The inequality of the crank angles for different positions 
of the piston attains its maximum value at the j stroke and 
gradually fades out at the extremities, and since we have 
equalized the cut-off for the \ stroke, it only remains to per- 
form the same office for the maximum cut-off before we 
practically equalize the motion for all intermediate gears 
between the full and mid gears. Our next step, therefore, 
will be to return to Fig. 29 and map on it the four positions 
of the eccentrics for the maximum cut-off. The third col- 
umn of the Angular Advance Table gives the maximum 
cut-off angle for the return stroke, which in the present in- 
stance =148°, and the Stroke Table shows that the forward 



116 



LINK NO 



stroke angle is 4^° less than the return, or=143|°. With 
these angles known, the four positions for the maximum 
cut-off may be readily laid off with a protractor, but the 
nature of the case enables us to present a more rapid solu- 
tion. From C F (Fig. 33) lay off an angle of 143f °. This 







Fig. 33. 








0.9ffl£ 


jk — 

s \\ 


~4x 

/ s >NT 

/ ^ux* 




\ \ 

\ \ 
\ A 






\ ySl 


1 \ j i CENTRAL UNEOF MOTION 


\»L 




\V i x W / 

— B\ Y 




JO 





locates the forward eccentric position 0.92/^ in the forward 
stroke. On the return stroke the same eccentric will be 
found at the old point b. Take the distance 0.92/' from/, 
in a pair of dividers and lay it off from b in order to find 
0.92&. In like manner take that from/ to B and lay it off 
from B, giving thereby b 0.92 the last one of the four maxi- 
mum cut-off points sought. With these points as centres 
and the length of the eccentric rod as radius sweep indefi- 



-0- 



>: 



i, 




LINK NO. I. 117 

nite arcs (as shown in Figure 34), on which the link tem- 
plate may travel in the full gear. 

IV. TO LOCATE THE TUMBLING SHAFT FOR ACCOMPLISH- 
ING AN EQUALIZED CUT-OFF IN ALL GEARS. 

Slide the link template with its eccentric rod pins on the 
elements 0.92/; 0.92 b, until its link arc comes in contact 
with the lap or cut-off point I (position No. 5) and mark the 
point S 4 occupied by the stud. 

Again, slide the template on the return stroke elements 
/0.92 ; b 0.92 until its link arc is in contact with the other 
lap point V, and mark the stud position S 5 . Join the points 
S 4 S 5 by a line c 2 c% which is found to have an inclination to 
the central line of motion of about 5° instead of parallel- 
ism* as with c c. 

By projecting the eccentric position points to the oppo- 
site side of their circle, sweeping indefinite elementary arcs 
with the eccentric rod as radius, and applying to them the 
link template, a corresponding set of stud locations S 2 , S 9 , 
S 6 , S T (Fig. 35) may be found for equal cut-off in the back 
gear. But such efforts are uncalled for in the class of mo- 
tions just described, because their back motion will be a 
precise counterpart of their forward motion, consequently 
the latter may be reproduced from the former, as in Fig- 
ure 35. 

Having thus determined 8 positions of the centre of sus- 
pension for equal J strokes and maximum cut-offs, it only 
remains to sustain the hanger in such a manner that for the 
different elevations it will sweep arcs passing through all 
of these points. Arcs of intersection formed with an as- 
sumed length of hanger as radius and these points as cen- 

* Parallelism might be secured by moving the stud S to within a distance t 
of the link arc (see Fig. W), but such a change would destroy the equality of 
the \ stroke cut-offs. 



118 LINK NO. I. 

tres will locate the points Ji and 7i\ and in like manner the 
tumbling shaft arm will determine its centre of shaft T.* 

Y. TO FIND THE LEAD OF THE FORWARD AND RETURN 
STROKES IN THE FULL GEAR. 

Having swept with the hanger an arc & & (Fig. 36) upon 
which the stud travels in the full gear of the link, slide the 
template on the forward lead elements F, B, until its stud 
lies at S 7 in the full gear arc & c% and mark the point d in 
which the link arc then intersects the central line of motion. 

In like manner slide the template on the return stroke 
elements./, b, and mark the intersection d z . 

The distances of these points from the lap circle will 
equal their respective leads. Thus in the forward stroke 
the lead equals Id in the full gear, but I d' in the mid gear ; 
while V d* equals the lead opening of the full gear return 
stroke, but V d 2 of its mid gear. In the present case both 
mid-gear leads were made equal to each other. Their slight 
variation in the full gear has absolutely no effect on the 
motion. 

VI. Extreme travel and slip of the link. 

Referring to Fig. 34 we observe that the forward eccen- 
tric attains the extreme points of its throw at D and E on 
the central line of motion at which times the backing 
eccentric occupies the positions T and U. [The latter 
points may be laid off from D and E with a pair of divi- 
ders set to the distance F &.] By sweeping the elementary 
arcs of the eccentric rod pins for these points and adjusting 
the template thereto, we obtain the positions Nos. 9 and 10 

* If the ratio of crank to connecting rod had been that of 1 : 5 or 6, the lines 
c 2 c 8 , c 3 c 3 would have had a greater inclination to the central line of motion, 
thereby removing h and h 3 to h 4 and h h , and depressing the shaft to some im- 
practicable point T 2 , where it would have been brought in contact with the for- 
ward eccentric rod when the link was in the back gear. The proper adjust- 
ment for such a case will shortly receive our attention. 



Central I. in.- of Motion 



FICURE36 




Liu.- ,,C M 




MODIFICATIONS. 119 

(Fig. 37) and are able to mark the extreme points Q, p, of 
the rocker arc which are separated by a horizontal distance 
equal to the extreme travel. 

For position .No. 8 the fixed point m on the template 
attains its maximum elevation above the link arc, and now, 
at the extreme throw, its greatest depression below that arc. 
The maximum slip will consequently equal the distance 
from p to o on the link arc. This slip grows less and less 
the nearer the stud approaches the rocker pin, and if the 
intention should be to use the link principally in the J 
gear this amount of slip would not prove detrimental. 



MODIFICATIONS. 

We have thus far, as concisely as possible, presented a 
geometric method for determining the proportions of all 
link motions, similar to those illustrated in Fig. 22. But 
its application cannot be considered universal, until certain 
expedients are explained, by which some of the results may 
be varied at will and also the motion corrected, when the 
ratio of crank to connecting rod is other than that of 1 : 7£. 



I. HOW TO KEDUCE THE SLIP. 

In the link motion of Fig. 37 the greatest slip occurs in 
the fall gear and the least in the mid gear. Now it fre- 
quently happens that after designing a motion the maximum 
slip is too great for practical purposes and the query arises : 
what change should be made for effecting its reduction ? 

There are four varieties of alterations capable of accom- 
plishing this object, which we will here mention in the order 
of their relative efficiency. 



120 MODIFICATIONS. 

1st. Increase the Angular Advance. 
2d. Heduce the Travel. 
3d. Increase the length of the Link, 
4th. Shorten the Eccentric Hods. 

Any one or more of these agencies may Ibe employed at 
the discretion of the designer and a more perfect motion "be 
produced. Thus we could diminish the slip to \ of its pres- 
ent value, by either increasing the angular advance to 30°, 
or by reducing the travel to 4 inches. Of course any such 
change involves an entire reconstruction of the motion in 
accordance with the principles already explained. 

II. HOW THE SLIP MAY BE DISTEIBUTED. 

Referring to Fig. 24 we observe that the general tendency 
of the fixed point m is to move in an arc the reverse of that 
pertaining to the rocker pin, while n traverses one more or 
less parallel. The maximum slip of the forward gear con- 
sequently exceeds that of the back gear. These quantities 
can be equalized in great measure by placing the stud, not on 
the central line/ S between./ and b but, upon some parallel 
line nearer to /than to £>, usually from 2 to 2^ inches above/ 
S. In such case the proper location for the stud is found 
by first drawing such a suspension line upon the link tem- 
plate, then sliding the template to the positions Nos. 3, 4, 
5 and 6 for the forward motion, and locating the line in 
question at each of these positions. Make similar locations 
(found with the proper arcs) for the back motion. Finally 
locate the stud for the full gear forward in such a manner 
that the line c 2 c 2 joining its points shall be parallel to the 
central line of motion. Two or three trials may be neces- 
sary before a suitable height for the suspension line above 
J S is obtained. This mode of suspension is frequently 
adopted on locomotive link motions. 

On the other hand, where no importance is attached to 



MODIFICATIONS. 121 

the accuracy of the back motion, the slip may be greatly 
diminished by inclining the rocker arms to each other (Fig. 
28) so that the arc r r of the pin shall, instead of preserving 
a state of tangency to the central line of motion, intersect it 
in a similar manner to the path of the point ra, Fig. 24. 
This method can be employed with advantage in designing 
marine link motions. 

III. Short connecting rods. 

If the ratio of crank to connecting rod had been assumed 
at 1 : 4^ instead of 7J, the position of the stud S found as 
before for equalized cut-off at the \ stroke, and the template 
slid to the positions 5 and 6, the change would have im- 
pressed on the line c 2 c 2 an inclination of 18° (instead of 5°) 
to the central line of motion. This would have rendered it 
impossible to equalize the motion in the ordinary way for 
more than one direction of the crank, without bringing the 
tumbling shaft and eccentric rods in conflict. But if the 
aim be simply to equalize the forward without regard to the 
back motion — a very common practice — no special difficulty 
will be experienced in hanging the tumbling shaft to even 
this case, for the point h s , Fig. 35, would then be left out 
of the account. 

There exists, however, a method of equalization which cor- 
rects the difficulty for both the forward and the back gears. 
It is clear that the tumbling shaft is employed most conven- 
iently and successfully, when it sustains the hanger in such 
a manner as to guide its vibrations in arcs practically par- 
allel to the central line of motion. Hence if we wish the 
link to conform with this condition it will be necessary to 
raise the template from position No. 6 of Fig. 34 to No. 11 
of Fig. 38 in which the line c 2 c 2 becomes parallel to the 
central line of motion. This elevation moves the lap point 
V to I 2 giving thereby a smaller lap circle 1 1 2 from which to 



122 MODIFICATIONS. 

determine the lap, and at the same time increasing the lead 
opening of the return stroke. The position A of the rocker 
is thereby carried to a point a more remote from the shaft, 
and the lead opening of the return stroke in the mid gear 
becomes greater than that for the forward gear. But we 
have already seen that whatever inequalities of lead open- 
ing may arise in the full gear, none can be tolerated in the 
mid gear. Nor is there an occasion for their existence, be- 
cause the linJc arc may be struck with a shoeter radius 
than the distance from the shaft to the rocker and all such 
inequalities be entirely eliminated. 

Take in a pair of compasses, the radius A d' of the mid- 
gear travel and strike the circle d* d h about the new 
position a of the rocker. To this the link arc must be 
tangent when the template is placed at the mid-gear position 
No. 1 and 2. Bring the template to position No. 2, mark 
the fixed points m and n of the full gears on the paper, and 
then search for a radius, having its centre in the central line 
of motion, whose arc shall embrace the three points 
m, d 5 , n. 

In the present extreme case the radius equals 41 J" 
against 49 J" employed with the ratio of 1 : 7 J. The two 
little cuts Y and Z, Fig. 39, illustrate the character of the 
lead openings before and after the change of the link arc 
radius. 

Having thus determined the true radius for the link arc 
a new template should be constructed, and all the locations 
made which are appropriate to the template positions Nos. 
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, under the new conditions, just as 
though no previous investigation had taken place. 

The result will be a motion capable of ready suspension 
from a tumbling shaft, with perfectly equalized cut-offs, 
with port openings varying to a slight extent in the full 



('(Miii;.! f.iue of Motion 





FIGURE 39 



MODIFICATIONS. 123 

gears but precisely equal in the mid gear, witli a forward 
stroke lead opening increasing from I d (Fig. Z) in the full 
to I d* in the mid gear, and with a return stroke lead, open- 
ing gradually from I 2 d z in the full to I 2 d 5 in the mid gear. 
Both these lead openings will be exactly equal to each other 
in the latter gear. It will be observed that all the inequal- 
ities of the motion are thus brought in the full gears, the 
very position where their influence is the least injurious. 

Of course it is not pretended that great inequalities of 
port openings are admissible in the full gears, unless the 
smallest of these openings shall exceed the 0.6 or 0.9 area 
(mentioned on page 23), in which case the magnitude of 
their difference becomes a matter of little importance, be- 
cause the wide opening will then admit no more steam than 
the narrow. But since the 0.6 or 0.9 area must be reached 
before the mid gear is attained, where the areas become 
equal, it is desirable to have as little irregularity in the 
other openings as possible. 

In reference to the lead opening, it is not unusual in lo- 
comotive " stationary -link" motions to give a constant 
lead of \ inch, where one increasing from ^g" or an |" in the 
full gear to §" in the mid, would be employed under like 
circumstances for a shifting link motion, and so far as can 
be discovered both motions are productive of equally good 
results. Hence we fail to perceive the force of objections 
so frequently urged against a slightly irregular lead, but 
believe that within proper limits resort should be had to 
this most efficient means for correcting the inequalities due 
to a short connecting rod. The recommendation, however, 
must be qualified for marine engines, whose more massive 
reciprocating parts require equal admissions for bringing 
them smoothly to a state of rest at the extremities of the 
stroke. For all such it is better to equalize the lead open- 



124 MODIFICATIONS. 

ings, at least in the full gear, and as far as practicable the 
cut-offs for the same, paying bnt little attention to the back 
gear. 

It has doubtless been observed that throughout the pre 
vious investigation no allusion has been made to the equal- 
ity of the exhaust closure, and no direct effort put forth for 
its conservation. The omission was intentional, simply be- 
cause the very process of equalizing the cut-off incidentally 
accomplished this object. In proof of which, it is only ne- 
cessary to consider that the neutral position (A) or exhaust- 
closure point lies exactly midway between the cut-off points 
Z, l\ so that if the motion be corrected for the latter when 
these are near each other, it must become practically per- 
fect for the former. But if the maximum cut-off should 
take place at about the f stroke of the piston, the lap points 
I and 1} would be widely separated, and probably give rise 
to a. marked inequality of the exhaust closure at the mid 
gear. Since irregularities of closure and release produce a 
greater impression on the motion when they occur at the 
mid rather than at the full gear of the link, and since it is 
possible by means of inside lap and clearance to correct 
them for either of these gears, it will be well to determine 
the extent of the inequality for the mid gear, and regulate 
accordingly the position of the exhaust chamber with ref- 
erence to the edges of the valve. To determine this correc- 
tion, bring the link template to one set of the half- stroke 
elements (Fig. 32) and slide it thereon until the link arc 
stands over the exhaust-closure point A (or <z, as the case 
may be). Mark the position of the stud S, and through 
this point draw a line parallel to the central line of motion. 
Next move the template on the other set of \ stroke ele- 
ments until the stud reaches the line just determined. 
Mark the point in which the link arc now intersects the cen- 



MODIFICATIONS. 125 

tral line of motion, and measure the distance of such inter- 
section from A. The required correction will be \ of this 
quantity. If the point falls on the forward side of the 
valve stroke it indicates that the exhaust chamber must be 
moved bodily this amount towards the forward edge F (Fig. 
11) ; but if on the back, towards the back edge N. 

IY. ECCENTEIC EOD PINS BACK OF LINK AEC. 

Judging from the frequency with which mistakes are 
made in the location of the eccentric rod pins, one is apt to 
conclude that most Designers regard their arrangement as 
a mere matter of caprice, and as having little or no bearing 
on the symmetry of the motion. This, however, is by no 
means the case, for each combination has its own appropri- 
ate method of attachment. A connection of the pins back 
of the link arc is best suited to a motion like that of Fig. 22, 
because it tends to hasten the speed of the rocker pin in the 
forward stroke, an object usually accomplished by raising 
the link at the expense of slip. 

The upper part of Fig. 34 has been reproduced in Fig. 
40 for the purpose of explaining this peculiarity of Link 
No. 1. By erecting perpendiculars to the central line of 
motion through the cut-off points I, l\ and by measuring 
from the same line, the respective distances of the eccentric 
rod pin/, for the 0.92 cut-off elements, we discover that the 
forward stroke distance T is much less than the return 
stroke R, and that if T was equal to R the rocker pin 
would be carried beyond Z, thereby delaying the cut-off of 
the forward stroke which now it hastens. In reality the 
slip is avoided by elevating the eccentric rod pin instead of 
the link arc. The advantage gained by this feature is very 
great, for while it tends to equalize the motion it reduces 
the slip of the link and renders easy the work of suspension 
from a tumbling shaft. 



126 



MODIFICATIONS 



In locomotive practice the distance of the pins' removal 
from the arc varies Ibetween 2{ and 3 inches. For marine 
work the limits are, in general terms, double these quan- 
tities. 

Fig. 40. 




The principal fact to be borne in mind is that, within 
suitable limits, the greater this distance the more readily 
can the motion be equalized. 

From the foregoing we perceive that Link No. 1 is ap- 
propriate to a motion requiring acceleration for any cut-off 
point beyond the neutral position A, and having its small- 
est crank angles laid off between the link and centre of the 



MODIFICATIONS. 127 

main shaft (as in Fig. 29). The four typical forms of such 
motions are here presented with a suitable arrangement of 
the parts, when the link is dropped in the full gear forward, 
for a positive motion of the crank. But if a negative mo- 
tion lbe demanded, it is only necessary to transpose the en- 
tire motion so that the cylinder comes on the opposite side 
of the shaft, in other words to take the power off the oppo- 
site extremity of the shaft after first turning the engine end 
for end. 

It was remarked (page 57) that the crank angles of a 
back-action engine are invariably the reverse of those com- 
mon to one of direct action ; hence, if we wish to preserve 
the identity of the motion in laying off a figure like 29 for 
such an engine, it will be necessary to locate the initial po- 
sitions F and B of the eccentrics opposite to those proper 
for a direct action, and apply thereto either of the two 
schemes offered in the Diagram. 



EXAMPLE. 

The following dimensions have been taken from a most 
successful freight engine ; their application will serve to 
familiarize the student with the principles of the foregoing 
method : 6 driving wheels, 57 inches diameter. Outside 
cylinders, 18 inches x 22 inches. Connecting rods 86 inches 
in length. Ports 15" in length ; steam, If" wide ; exhaust, 
3". Diameter of eccentric circle =5 inches. Maximum 
cut-off=0.8 of stroke. Mid gear lead=i 5 g inch. Rocker 
from shafts 55 1 inches. Length of rocker arms =9 inches. 
c. to c. of eccentric pins=13 inches. Tumbling shaft arm= 
18 inches. Hanger=13J inches. Pins back of arc = 8 J 
inches. 

Required. — Radius of link, distance of point of sus- 
pension back of link arc, lap of valve, full gear lead, and 
location of the tumbling shaft. 



LINK No. II, 



Commonly known as the " Open Link," is specially 
adapted to cases in which the link acts directly on the valve 

stem without the intervention of 
a rocker, as peculiar to British 
practice. It differs from No. 1 in 
the location of its eccentric rod 
pins. These, instead of occupy- 
ing stations back of the link arc, 
reside at points / and b beyond 
the extreme positions m and n 
of the link block. They conse- 
quently move a greater distance 
than the latter points, and in 
order to preserve the same travel 
of valve the eccentric circle must 
be enlarged. 

In locomotive practice the dis- 
tance between eccentric rod pins 
/ and b varies from 16" to 20". 
The diameter of the eccentric circle varies from 5^ to 7 
inches, and the working points m and n usually about 3" 
from the pins. The template for this form of link is illus- 
trated by Fig. 41. 

This link No. 2 is specially adapted to a motion re- 
quiring acceleration for any cut-off point beyond the neu- 
tral position A, and having its greatest crank angles laid 
off between the link and centre of the main shaft. It will 
be remembered that with Link No. 1 (Fig. 40) the smallest 
crank angles occupied such a station, and the eccentric pin 




LINK NO. II. 



129 



was elevated to the position /, making the distance T less 
than R. If, however, the greatest crank angles had occu- 
pied this position, the element / would have been removed 



Fig. 41. 




to some line / 4 nearer the shaft, while the link would have 
been depressed and slip increased in the endeavor to make 
T=R. But the equality of these terms is established when 
the link arc passes through the centres of the eccentric rod 
pins ; hence, a " Box Link," having its pins over the work- 
ing points m and n, will be found better adapted to this 
position than Link No. 1, yet it only supplants the more 
readily-constructed open link, when it becomes important 
to retain the throw of the eccentric at its lowest limit. 

As with Link No. 1, so with No. 2, there are four 
9 



130 CONSTRUCTION. 

schemes to which the motion is peculiarly applicable. 
These are given in the accompanying Diagram for the posi- 
tive motion of direct and Iback-action Engines. As hereto- 
fore explained, their negative motion may be obtained by 
transposing the cylinder and link motion to the opposite 
side of the main shaft and taking off the power from the 
other extremity of the same. When, therefore, it has been 
decided that an engine shall have a direct or back-action 
arrangement of the connecting rod, the link to act through 
or without a rocker on its valve, and its forward motion to 
be positive or negative, then an appropriate arrangement 
of the link can be at once selected from these two diagrams, 
and the side of the shaft determined, on which the cylinder 
should be placed, to secure the desired crank motion when 
the link is dropped in the full gear forward. 

It should be observed here, that the lower part of the 
link is never used in a horizontal engine to impart a forward 
motion because the weight of the overhanging or sustained 
parts tends to render the motion unsteady. 



CONSTRUCTION. 

To find approximately the throw of the eccentrics and 
their angular advance for a given travel of the valve, length 
of link and position of the working point. 

Describe about any point C (Fig. 42) on a vertical line F 
E, a semi-circle E H with a diameter equal to the proposed 
travel of the valve ; from C lay off C P, the extreme dis- 
tance of the working point from the eccentric pin, also C S 
the | length of the link. With S as a centre describe the 
arcs C /, P m, and b R. Suppose now the cut-off must 
take place at 0.78 of the stroke, then from the Travel Scale 



CONSTRUCTION 



131 



we learn that the trial angular advance should be 28°. Lay 
off C B 28° from F C and produce the line D B passing 



Fig. 42. 



12A"=CUT OFF, 0.78 'STROKE 
OH AW ADVAHCE .05.28° 




through the point of intersection B parallel to F R. Strike 
a trial eccentric circle ;'FK about the centre C. Take the 
distance between its two intersections D and F in a pair of 
dividers and lay it off twice from G, giving the point K. 



132 APPLICATION OF LINK NO. II. 

Through K draw a line parallel to C E and determine its 
intersection b with the arc E b. Draw a right line through 
b and the extreme travel point m. If now / should be 
found in the tangent line through j to the eccentric circle, 
it would prove that the diameter of this circle had been 
assumed correctly. But if it falls without the assumed 
circle, this diameter must be increased. Conversely any 
point within requires a diminution of the same. Thus the 
point e indicates that the diameter of its circle j g k has 
been assumed too large. 

Having secured the correct diameter of the eccentric 
circle, join the points D and C by a right line and measure 
its inclination to the line F E. We thus obtain 19° the 
true angular advance of the eccentric for accomplishing 
the desired cut-off. The principle involved in this construc- 
tion is that when one eccentric produces its extreme throw D 
(Fig. 33) the other will be separated from its like position E 
by the horizontal distance of T, which always equals double 
the angular advance. Although this construction does not 
claim strict accuracy, it will be found to answer all practi- 
cal purposes. 



APPLICATION" OF LESTK NO. II. 

For illustrating the process of manipulation peculiar to 
this form of link, we will assume the following terms : 
Crank and rod ratio =1 : 6 \. 
Cut-off at 0.8 of the stroke. 
Travel of valve =4f inches. 
Valve stem from shaft =5 ft. 
Distance between eccentric rod pins =18". 
Extreme working points, 3" from pins. 
Mid-gear lead opening =| inch. 



APPLICATION OF LINK NO. II 133 

By a construction like that of Fig. 42, an angular ad- 
vance of about 16° and eccentric circle of 6| inches diameter 
are found to conform with the above conditions. If now 
the connecting rod and link motion act directly on the piston 
and valve the initial position of the motion will be that pre- 
sented in the first Figure of the applications, and the 
four starting points F, B, /, &, together with the four \ stroke 
points of the eccentric circle, may be mapped in a similar 
manner to Fig. 29 ; while the four 0.8 cut-off points should 
be laid off by means of a protractor from the lines F C, B 
C,/C, andJC. 

Having mapped these twelve important positions and 
constructed a template like Fig. 41 the next step will be to 
follow the journey ings of the link arc and locate the tum- 
bling shaft in a manner precisely analogous to that pursued 
with Link No. 1 : 



Find 



1st. The mid-gear travel =d } d 2 . 
2d. The lap A I for a given mid-gear lead. 
3d. The position of the stud for equal \ stroke 
cut-offs of the piston. 



This form of link is more generally suspended from the 
upper eccentric rod pin than from a point midway between 
the two, and has the tumbling shaft below the central line 
of motion ; but by marking the various locations of both 
pins, as well as the centre line J, we will be able to select 
the most appropriate of the three suspensions. 

Let us follow first the central suspension. We find that 
by locating the stud on the arc, the line c c of its motion, 
for the ^ stroke cut-off, becomes parallel to the central line 
of motion, a condition suited to ready suspension. But on 



134 APPLICATION OF LINK NO. II. 

dropping the template to the full gear cut-offs the stud as- 
sumes the positions S 4 S 5 , Fig. 43, whose line c 2 c 2 has so 
great an inclination to the central line of motion, that it 
would he next to impossible to successfully hang it from a 
tumbling shaft and accomplish equal cut-offs in all gears. 
We must consequently resort to a change of link arc radius 
and unequal full gear leads (as in Figs. 38 and 39) in order 
to establish perfect equality. To do this, raise the link arc 
so that the stud shall occupy a location S 6 * thereby bringing 
& & more nearly to a state of parallelism with the central 
line of motion. Mark V the new lap point ; strike a new 
lap circle I V with neutral position a, nearer to the main 
shaft, and about this point describe the mid-gear travel cir- 
cle giving new points d* d b through which the link arc must 
pass for the mid gear. Bring the template to position No. 
2, as in Fig. 31, mark the eccentric pin points/ and b ; then 
search for a radius whose arc shall pass through the three 
points/', d\ b. This radius will always prove greater than 
the distance from the centre of the shaft to the neutral po- 
sition A instead of less, as found with Link No. 1. 

Having obtained a correct link arc, cut out a new tem- 
plate like Fig. 41 to represent it, and reconstruct the entire 
motion. The new radius will equal 5 ft. 7". The corrected 
lap = lg 1 ^ inches. The lead for the forward stroke, increases 
from | to | in the mid gear, and from T 3 g to* f for the return 
stroke. The lines of suspension pin motion c, d, <? 2 , c 3 may 
converge, as in the present instance, towards some point 
beyond the link. In such case the tumbling shaft should 
be placed on the side of the convergence. 

If, however, the link is suspended by the upper eccen- 
tric rod pin, the forward gear paths of the suspension pin 
motion will be represented by the lines h, 7i\ and the tum- 
bling shaft will lie below the central line of motion ; but for 




t>08 



APPLICATION OF LINK NO. II. 135 

the lower eccentric rod pin, the lines will become e, e\ t\ 
and its tumbling shaft will stand above this line. 

The judgment of the designer will in every case decide 
to what extent the lead openings should vary in the full 
gears, what inequalities of cut-off are admissible, and 
whether or not the motion should be equalized simply for 
the forward without regard to the back gear. 



While attempting to analyze the peculiarities of various 
existing link motions, the investigator usually finds that 
among other dimensions, only the lap and mid gear lead 
are given, and that no allusion is made to the angular 
advance, or to the maximum cut-off. To solve such cases, 
he is compelled to work the problem as it were, backwards. 
On the central line of motion he plots the lap and lead, as 
on Fig. 32, places the template in the Nos. 1 and 2 positions, 
as in Fig. 31, then with the length of the eccentric rod as a 
radius and the positions of the eccentric pins as centres, 
strikes in the direction of the shaft indefinite arcs, whose 
intersections with the eccentric circle give the points F, B, 
f, b, (equi-distant from the central line of motion) and 
from these the desired angular advance can readily be 
measured. 



BOX LINK 



Although the mechanical construc- 
tion of this form of link is rather more 
difficult than that of No. 2, it serves 
the part of a good substitute when a 
short throw of the eccentric is required ; 
for with it the maximum travel of the 
valve always approximately equals the 
diameter of the eccentric circle. 

At times the box link can be em- 
ployed in positions appropriate to Link 
No. 1, but very rarely with those good 
results in respect to minimum slip 
which obtain with the former motion. 
On such occasions the stud usually lies 
— at some point beyond the link arc, de- 
termined by placing the link in the \ 
stroke cut-off positions, Nos. 3 and 4, 

and plotting the centre line^' as in Fig. 32. 

When, however, the box link is used in place of Link 

No. 2, the centre of suspension S generally falls within the 

link arc, or between it and the main shaft. 

The construction of these links varies ; in some instances 

the ribs are formed on the inside as represented, while in 

others, they are cast on the sliding block and overlap the 

link plates. 




STATIONAEY LINK. 



This form of connection between the valve and -eccen- 
trics is specially applicable to those circumstances in which 
the former requires no rocker. The mutual relation of 
the parts will be clearly perceived from an examination 
of Fig. 44 which illustrates one of the most successful 
methods of suspension. * The eccentrics stand in their usual 
location for a direct action motion. The main link is hung 
from a fixed point by a short bar called the " suspending 
link" and the link block connected with the valve stem 
through the " Radius Rod " m d). By means of a reversing 
combination the block may be carried to any point between m 
the full gear forward and n the full gear back. But since the 
link arc is always struck with a radius equal to the length of 
the rod m d\ having its centre at d) and d 2 in the central line 
of motion, when the crank occupies the zero or 180° location, 
it must be evident that the block can be moved from one 
full gear to the other without altering the position of the 
points d ] or d% consequently the lead opening will remain con- 
stant throughout the motion, the same as in Fig. 17. Now 
it has been invariably the custom to simply define a station- 
ary link motion as "one in which the lead is constant" 

* For convenience of observation, the cross sections of the valve and seat 
have been revolved to a plane at right angles to their true position. 



138 STATIONARY. LINK. 

leaving it to be inferred that the angular withdrawal of the 
crank from its zero position at the moment of pre-admission 
must also be a constant quantity, whereas in reality this 
lead angle increases just as much for a stationary link 
motion as for a shifting one. The only difference between 
the two is that the lead opening of the stationary link 
motion is more ample and the angle slightly greater, for all 
except the mid gear, than with the shifting link motion. 
But this distinction has been so clearly drawn in Part III. 
that further remark can scarcely be necessary. Unlike the 
shifting link motion, however, the lead opening is not 
dependent on the arrangement of the eccentric rods, for 
these may either be crossed or opened without altering the 
result. But for the purpose of meeting the other conditions 
of the motion an arrangement like Fig. 44 should be 
adopted. 

As a general thing more attention is paid to the equali- 
zation of the cut-off and reduction of the slip in the forward 
than in the back gear. For the accomplishment of this 
object, the centre of the link should be dropped below the 
central line of motion, the angular advance of the backing 
eccentric slightly reduced and the backing eccentric rod 
lengthened. 

The simplest method by which the student can obtain a 
clear idea of the action of the parts, in a stationary link 
motion, will be for him to take the dimensions of some suc- 
cessful motion, cut out a proper template for the link and 
trace its journey ings throughout the different gears in con- 
formity with principles already laid down for the shifting 
link motion. 

The following dimensions (in absence of others) will 
answer such a purpose : 




/f "^ns - 



Mil 



FIGU 





l 



FIGURE 45 



f'rtii jhl'ij'] __ _- 




STATIONARY LINK. 139 

Diameter of piston =18 inches. 

Stroke =24-'' ; Connecting rod=91". 

Katio = 1 : 7J. Throw of eccentrics = 2 § ". 

Forward eccentric angular adv. =27J°. Rod=57§". 

Backing eccentric angular adv. =26°. Rod=58". 

Eccentric rod pins 12-|" apart, 3" back of arc. 

Centre of suspension 1|" back of arc, 1J" below line. 

Radius rod=37", Reversing link=ll^", Hanger=9". 

Tumbling shaft arm =18". Reversing pin 8'' back of arc. 

Lead=f", Steam port =2", Exhaust =3 J". 

Maximum travel about 4| inches. 

The Stationary Link is seldom found in American 
practice from the fact that all modern locomotives are built 
with steam chests on top of their cylinders, instead of at 
the side. On stationary engines, the link and governor are 
occasionally used conjointly ; in such instances the station- 
ary link will be found best adapted to the requirements of 
the case, because its radius rod imposes a far lighter duty 
upon the balls of the governor, than the shifting link with 
its rods, hanger, and additional friction of eccentric straps. 



ALLAN LINK MOTION 



The discovery of this motion was a natural sequence to the 
invention of the shifting and stationary links. By it a com- 
promise has been effected between the leading features of both 
motions, resulting in a more direct action and perfect balance 
of the parts together with a reduced slip of the link block. 
One mode of suspension, for the link in the full gear forward, 
appears in Fig. 45, in which the cross sections of the valve 
and its seat have been revolved for the purpose of more 
plainly exhibiting their relative positions. The locations of 
the point of suspension and attachments of the eccentric 
rod pins upon or back of the link arc are quite as variable 
for this, as for the shifting link motion ; and the requirements 
of the other details generally indicate whether the reversing 
shaft should be placed above or below the central line of 
motion. 

In proportioning the parts, the main object is to move 
the link and radius rod (when the crank stands at the zero 
or 180° locations) in such a manner that the link arcs 
peculiar to each motion shall always be tangent to each 
other. In this case all the locations of the link block will 
be found in one and the same straight line. This peculiar- 
ity has given rise to the title " Straight Link" motion 
expressive of the form of the link. 



ALLAN LINK MOTION. 141 

The radius rod and main link are supported by rods 
from the reversing shaft arms, and the inequality in the 
lengths of the latter, which is essential to a proper suspen- 
sion of the parts, incidentally tends to equalize the weights 
resting on the opposite sides of the reversing shaft, thus 
greatly facilitating a change of the motion from one full 
gear to the other. 

Well-schemed motions of this type practically preserve 
the characteristic feature of the stationary link, viz., a con- 
stant lead ; yet from the nature of the case they possess at 
times slight inequalities in one or both of the full gears. 
These, however, are quite insignificant for a relatively long 
radius rod and short travel. 

The ratio between the long and short arms of the re- 
versing shaft may be readily determined for any given 
travel, angular advance, length of eccentric rods, link and 
radius rod, by placing the template in the No. 1 and 2 posi- 
tions (Fig. 31), marking the mid-gear travel d' d% sweeping 
indefinite arcs through these points with the radius rod, and 
drawing down the template, or centre of suspension, from S 
to S 8 until its straight line intersects these arcs in points m, 
m 2 . Then map the radius rod m d\ m 2 d 2 giving the points 
% v) of the reversing rod pin above the central line of mo- 
tion. The centre I of the link arm pin must fall as much 
below the horizontal line through the reversing shaft R as 
S 2 does below S. In like manner the pin h of the other 
arm must rise as far above the horizontal as u does above 
the central line of motion. Finally, draw I h of length suf- 
ficient to accommodate the details of the shaft, and we have 
at once the proper dimensions for the reversing shaft arms. 

It should be observed that the tendency of m 2 is to drop 
below m and thus distort the motion, but this will be ob- 
viated if the two are brought into one horizontal line inter- 



142 ALLAN LINK MOTION. 

mediate between such, stations. The change will result in a 
slightly increasing lead, as 'is common with the shifting 
link motion. 

The following dimensions can be employed for an inves- 
tigation of this class of motions : 

Diameter of cylinder =16". 

Stroke=24' ; ; Connecting rod=87" ; Eatio=l : 7|. 
Throw of eccentric=24" ; Angular advance=26°. 
Eccentric rods=39^ inches. 
Radius rod =47", connected 7" back of link. 
Box link, suspended by stud at centre with eccentric 
rod pins 10" apart. 

Suspending rods both 18 ' long. 
Reversing lever, long arm =6". 
Reversing lever, short arm =2 J". 
Mid-gear lead = \ inch. 
Steam port=lJ" ; Exhaust=2|". 



If the examiner desires to analyze any stationary or 
straight link motion already constructed, having a given 
lap and lead but no specified angular advance, he should 
work the problem backwards, as follows : First locate the 
four cardinal points d', Z, V, d% and sweep their arcs with 
the radius rod ; then place the link in the positions Nos. 1 
and 2, with the positions of the eccentric rod pins as centres 
and the length of the eccentric rod as a radius, sweep the 
four arcs, which must contain the points F, B, f, b, and 
describe through them the given eccentric circle, in such 
a manner that all the points of intersection will lie equally 
remote from the central line of motion. With these initial 
points determined, the investigation can proceed on the 
principles already explained. 



WALSCHAEKT LINK MOTION". 



This device groups two perfectly distinct motions — the 
one derived from a single eccentric, the other from the cross- 
head of the piston rod — in such a manner that their 
combined effect is, when the parts are well proportioned, 
quite analogous to the motion obtained from the stationary 
link. From the nature of the connection between the cross- 
head and the valve-stem, the motion can be more readily 
applied to an outside cylinder engine than to an inside one. 

The eccentric usually assumes the form of a return 
crank from the main crank pin, as shown in Fig. 46. Its 
centre then is found on a line at right angles to the crank 
arm. The angular advance becomes equal to zero, and 
hence, so far as the link will be concerned, the valve can 
have neither lap nor lead. The link oscillates freely about 
a fixed axis, and its arc has a radius equal to the length of 
the radius rod. This rod is moved from one full gear to 
the other, in the usual manner, by means of a reversing 
shaft with arms. From the extremity of a short arm, 
rigidly bolted to the cross-head pin, extends a union bar 
which is pinned to one end of the combination lever. By 
the aid of this lever, the eccentric and cross-head motions 
are so combined, that the latter virtually restores the angu- 
lar advance discarded while locating the eccentric, and 



144 



WALSCHAEKT LINK MOTION. 



consequently enables the valve to possess "both a constant 
lap and lead. 

The truth of this assertion will appear from an examina- 
tion of the lever elements (Fig. 47) for 12 locations of the 
crank arm. 



Fig. 47. 

6i' # 1J1.&H19 



% el 



tW 



It-- 



— ~-- AM 



JO. 



-^rSXr'- 



The subjoined dimensions will be found convenient for 
the construction of a trial example, in which of course two 
templates should be employed, one to represent the link, 
the other the combination lever : — 



WALSCHAERT LINK MOTION. 145 

Diameter of piston=18". 
Stroke=24" ; Connecting rod=100". 
Ratio=l : 8J. 

Axis of link 74" from centre of shaft and 15| above cen- 
tral line of motion. 

Eccentric rod pin 13" from axis of link. 
Radius of link and length of rod=42«|". 
Link block to end centre of radins rod =6". 
Long lever of combination arm =30". 
Cross-head arm drops 14 § inch3S. 
Connection for arm and lever=16". 
Throw of eccentric— 3| inches. 
Travel of valve (maximum) =4J inches. 
Lap=l inch ; Constant lead of \''. 
Steam port 1 J" ; Exhaust port=3". 

Cases will at times arise in which the distance between 
the centre of shaft and valve, will prove too contracted for 
a satisfactory arrangement of the parts after the manner 
shown in Fig. 46. In such instances the curvature of the 
link should be reversed, the radius rod made to lie between 
the link and shaft, and the valve stem lengthened, to adapt 
it to the new position of the combination lever. 

The Designer will find that his efforts, towards the equal- 
ization of the cut-off in the Walschiiert Motion, are attended 
with far less difficulty than similar ones with the shifting and 
stationary links. ' This peculiarity arises, from the intimate 
relation constantly maintained between the valve and piston 
motions, through the medium of the combination lever. In 
consequence of which, any undue acceleration or retardation 
of the piston motion is immediately accompanied by like 
effect in that of the valve, thereby greatly diminishing its 
capacity to derange the events of the stroke. 
10 



PART V. 



INDEPENDENT CUT-OFF, 



CLEAKANCE, ETC. 



INDEPENDENT CUT-OFF. 



It has "been demonstrated in Part I. that a very early 
cut-off is incompatible with the economic action of a single 
eccentric, for beyond the limit of about § of the stroke, the 
compression attending an earlier closure of the exhaust will 
usually furnish a resistance in excess of that required for 
neutralizing the momentum of the reciprocating parts. If 
therefore a more extended range of the cut-off should be 
demanded, for comparatively slow speed engines, other 
means must be sought by which it can be controlled with- 
out affecting the exhaust ; in a word independent valves 
must be introduced having a motion different from that of 
the main valve. For this purpose the parts are usually 
arranged as shown in Fig. 48. The valve A carries on its 
back two cut-off valves B B' and rigidly supports by pillars 
the surface plate H H on which a brass packing ring F F 
bears, enclosing a space D in communication with the con- 
denser through the pipe E. The partial vacuum formed in 
this space relieves the valve in great measure of the im- 
mense pressure exerted by the steam, and consequently 
reduces the friction as well as facilitates the starting of the 
engine. 

On the cut-off valve stem are turned a right and left 
hand thread, so that by revolving the same, the valves may 
be drawn closer together or separated by a wider distance 



150 



INDEPENDENT CUT-OFF 



according to the requirements of the cut-off. The main 
valve A has a lap, lead and exhaust closure appropriate to 
the value of the maximum cut-off, and permanently retains 



Fig. 48. 




these quantities throughout every variation in the point of 
cut-off brought about by the separation of the valves B B'. 
Its general design depends upon the range of the cut-off. 
For one varying between zero and about 0.6 of the stroke the 
combination shown in Fig. 48 is most suitable, where the 
outer edges c c, effect the closure of the port, and the valves 
have a motion directly the reverse of that peculiar to the 
piston. For cut-offs varying between 0.3 and 0.9 the stroke 
the inner edges e e should be made to perform this office, 
and the valves should have a travel coincident with that of 
the piston. Between the assigned limits such valves give 
sharp and decisive cut-offs for a proper ratio between the 
travels of the main and cut-off valves. When the outer 



INDEPENDENT CUT-OFF. 151 

edges are employed the travel of the cut-off valves should 
exceed that of the main valve ; "but with the inner edges it 
may equal or exceed it according to the degree of rapidity 
desired in the action. 

The relative motions of the valves, may for any required 
case be conveniently examined, by a method indicated in 
Fig. 49, and the travel regulated to meet the conditions of a 
good motion. The valves are here supposed to cut off with 
their inner edges but the process is equally applicable to 
the opposite relation. 1st. Stretch a sheet of paper and 
upon it draw the steam ports, exhaust port, bridges, and 
a circle f g representing the motion of the main valve's 
eccentric with an angular advance position R 1, also the \ 
stroke R 3, and the maximum cut-off R 4. Project these 
points to the line of the valve seat, thus giving the positions 
1, 2, 3 and 4. Secure a slip of paper X A with its base 
line A over the point 6, and draw the main valve with lap 
appropriate to the maximum cut-off precisely as in Part I. 
Make the steam passages S S convergent in order to econo- 
mize space. Secure a second slip W D as before shown, 
and above its base line D describe a circle Tij to represent 
the path of the eccentric acting on the cut-off valves. Its 
initial position will be found at R 1 the same relatively as 
the crank of the engine. From this lay off R 2, 3 and 4, 
making angles with R 1 equal to those found in the 
circle f g. These preliminary steps completed, our ob- 
ject will be to find the degree of separation required 
between the valves for the given cut-offs, their width, 
and also to what extent the. faces L L should be length- 
ened to prevent a fall of either cut-off valve. Suppose 
for instance the limits were J and J stroke, we first loosen 
the two strips W and X, place their base lines A and D at 
ISTos. 3 the J stroke locations for their respective eccentrics, 



152 INDEPENDENT CUT-OFF. 

and mark e for the point at which the cnt-off valve should 
stand to effect the closure of the steam port. Second, move 
the slips W and X until their base lines A and D correspond 
with Nos. 4," the other cut-off limit mark e" and it will 
appear that the valve stem must be rotated, until the cut-off 
valve B moves a distance n from its first position e. Since 
the right and left hand threads have one pitch, the other 
cut-off valve B' will be moved a like distance from the com- 
mon centre C. Third, the valves must be sufficiently wide 
to guard against a re-opening of the port before its final 
closure by the main valve. This distance may be found by 
placing the strips at the Nos. 4 positions and marking a 
point c on the strip W opposite the edge d ; when the length 
of the valve should at least equal the distance from e to c. 
Fourth, Place the strips W and X at the 1 JNos. 1 locations 
and we obtain substantially the extreme position of the cut- 
off valve with reference to the main valve which will indicate 
the proper extension for the faces L L. 

If other positions of the eccentric are interpolated be- 
tween 1, 2, 3, and 4, the relative motions may be accurately 
traced and the degree of port opening observed, so that in 
event of the latter proving inadequate, the diameter of the 
circle hj can be increased a suitable amount. It is cus- 
tomary in proportioning stationary engines with valves con- 
structed on this principle, to make the cut-off variable be- 
tween 0.3 and j the stroke, while the main valve is arranged 
with a lead angle of about 8° and a lap suitable to a cut-off 
of I the stroke. The resulting angular advance usually 
furnishes an appropriate exhaust closure. If, however, on 
trial the crank should not pass its centres smoothly, the 
angular advance of the eccentric must be increased or di- 
minished until the proper compression is discovered for 
counteracting the momentum of the reciprocating parts, as 



INDEPENDENT CUT-OFF. 153 

Fig. 49. 




well as lead opening for neutralizing the effect of lost 
motion. 



154 EQUALIZATION OF YALVE MOTION. 

In marine engines the cut-off valves act with their outer 
edges. The lap angle of the main valve is then taken at 
from 15° to 20 degrees, and the exhaust closure effected at 
about 0.9 the stroke, "by simply raising the link, until the 
eccentrics have virtually an angular advance of 35 to 45 
degrees ; in other words, by working the link in less than 
the full gear. The necessity of adjusting the eccentrics is 
thus obviated. 

When an engine is furnished with exhaust passages per- 
fectly distinct from those admitting the steam to the cylin- 
der, and the demands upon its power are quite uniform, 
the valves regulating the exhaust should be adjusted by the 
quantity of coal consumed. That is, the angular advance 
of their eccentric should, from time to time, be increased 
until at length the limit of greatest economy is attained. 
The result of course must not be judged by a computation 
of the indicator card, for that necessarily ignores the effect 
of the momentum of the reciprocating parts, since it mea- 
sures the power in the act of being applied and not subse- 
quently to the application, a distinction of great importance. 



EQUALIZATION OF YALTE MOTIOK 

The cut-off being produced by a valve independent of 
that regulating the lead, its equalization may be accom- 
plished without any of the difficulties incident to a single 
eccentric motion, where the slightest change in either event 
is immediately felt by the other. The desired result is ap- 
proximately obtained for a single eccentric motion, by sim- 
ply lengthening the cut-off valve stem an amount depend- 
ent on the ratio existing between crank and connecting rod. 



CLEARANCE. 155 

If, however, the valve moves under the influence of alever 
attached to the reciprocating parts of the engine, as in rig. 
52, the motion will become equalized by virtue of the irreg- 
ularities thus introduced to the valve motion (a counterpart 
of those peculiar to the piston) and any slight inequalities 
of the main valve will be counteracted by a change in the 
length of the cut-off valve stem. The lead should be made 
equal for both faces of the main valve, and if neither the 
single eccentric nor link by which the latter is operated 
accomplishes an equalization of the exhaust closure, then a 
suitable amount of inside lap and clearance (as explained 
Part II) should be given to the exhaust edges of the valve 
face. The cut-off equality of the main valve, in itself con- 
sidered, is of little consequence, hence the link should be 
arranged to give the smallest amount of slip attainable 
with an equality of the lead, and the cut-off should be reg- 
ulated solely by the cut-off valves. 



CLEARANCE 



This term is used to express, the extent of the space 
which exists between the piston at the extremity of its 
stroke and the valve face, or the cubic contents of the steam 
passage plus the unoccupied portion of the cylinder. 
Since for each stroke of the piston this space must be filled 
with steam, which in no way tends to improve the action of 
the parts, but rather increases the amount to be exhausted 
on the return stroke, it becomes desirable in long-stroke 
engines to locate the valve face as near the end of the stroke 
as possible, thus reducing the cubic contents of the passage 
and by its directness admitting the steam with a higher 



156 



FEICTION. 



initial pressure than could be obtained through a more tor- 
tuous channel. 

A convenient method for accomplishing this result, is to 
separate the valve faces F and 1ST by means of a stem, as 
shown in Fig. 50, and forming them either in the shape of a 

Fig. 50. 




letter Q laid on its side, or as small pistons. The former 
or D valve construction was much employed a few years 
since, but has been gradually supplanted by the more me- 
chanical arrangement of the piston valve. This, instead of 
being surrounded by packing in the valve case, carries its 
expansive packing in the same manner as an ordinary pis- 
ton. The steam is received either between the pistons, from 
a pipe P, giving the most direct admission to the cylinder, 
or externally from chambers e e. The parts surrounding 
the valves are well jacketed to prevent unequal expansion, 
and slight irregularities are compensated by the elasticity 
of the packing. 



FKICTIOE". 

The friction of a valve is quite independent of its surface, 
except so far as the latter may increase the area upon 
which the steam can exert an unbalanced pressure. 



REDUCTION IX TRAVEL 



157 



There are various expedients for relieving such pressure. 
Two of these have been illustrated in Figs. 48 and 50. A 
third consists in casting a standard in the exhaust port on 
which is bolted a concave plate, scraped to a bearing upon 
the inner surface of the valve, and holes drilled through the 
top admit the steam under the valve, which tends to relieve 
the external pressure. Besides these devices the valve is 
frequently mounted on steel rollers about If inches diame- 
ter resting on plates of the same metal, and thus the sliding 
converted into rolling friction. Heavy valves standing in a 
vertical position have additional rollers under their lower 
edge for supporting their great weight. 



REDUCTION IN TRAVEL. 

The work expended in friction depends directly upon 
the distance traversed by the valve. Hence, in marine en- 
gines every means possible should be employed to reduce 
this quantity to its minimum value. This object may be 

Fig. 51. 




attained by increasing the number of the steam ports two 
or three fold, so that \ or \ of the travel will suffice to open 
the same extent of port area. For a reduction in the travel 



158 LINK AND EECIPEOCATIIG 

of one-half, the parts are commonly arranged as shown in 
Fig. 51. In this the valve edges F and N are separated by 
a distance wide enough to admit two steam passages U, U, 
whose openings T T communicate with the inner ports but 
not with the exhaust. They are formed with a width equal 
to that designed for the port opening. The general propor- 
tions of such valves may be concisely expressed as follows : 

Total width of steam passage =2 S. 

Each port=S. Width of port opening =T. 

Exhaust port=4 S. 

Yalve faces F and N=S+lap of valve. 

Bridge W=J travel +lap+T+§ inch. 

Width of exhaust bridge B dependent on thickness of 
cylinder. 

Width of exhaust bridge b dependent on thickness of 
valve. 

Occasionally the travel is reduced still further by insert- 
ing a third port beyond the other two. When so arranged 
the outer faces F and N are extended and through them 
passages cut, which admit the steam to the cylinder, but 
remain closed during the period of exhaust ; consequently 
the two exhaust passages must be amply large to discharge 
the steam received through the three openings. 



LINK AND RECIPROCATING MOTION COMBINED. ' 

It was observed, while discussing the subject of link mo- 
tion, that the central line of motion might be inclined at any 
angle to that of the piston motion, without affecting the 
character of the valve action. Fig. 52 illustrates this pecu- 



MOTION COMBINED 



109 



liarity (for one position, namely, an angle of 75°) as applied 
to a "back-action engine having an independent cut-off. 
The line E F represents the central line of the link motion, 



Fig. 52. 




and Gr H a line at right angles thereto from which are laid 
off the 15 degree angular advances of the eccentrics. The 
eccentric rods being crossed, the lead of course diminishes 
from the full to the mid gear of the link, but as this is only 
employed in the full or immediately adjacent gears, the re- 
duction proves advantageous, since it enables the engineer 
to stop his engine by placing the link in the mid gear (see 
Fig. 26). The cut-off valves are operated by a lever I J 
connected through the link J K with the pin K, which is 
secured to one of the piston rods or to the cross-head in a 
direct-action engine. 

This valve motion might have been derived from an ec- . 



160 LINK AND EECIPEOCATING MOTION. 

centric with its normal position in the line E F, and acting 
on the valve through the medium of a rocker. The general 
conditions governing the motion have already been ex- 
amined. 

There are numerous other positions in which the link 
may he placed, and many other plans for connection with 
the valve, but it is believed that the typical forms have 
been presented with sufficient care and accuracy to enable 
the designer by their aid to accomplish any desired result. 

It may prove a source of regret to some, that the numer- 
ous class of automatic cut-off gears, now so extensively 
applied to stationary engines, should have received no 
special attention in this Work. The Author however, has 
considered it most expedient to confine himself to general 
principles and to subjects requiring a solution in every day 
experience, leaving with those who hold such monop- 
olies, and who alone can make use of them, the onus of 
explaining their principles and advertising their points of 
excellence. 



APPENDIX. 



FORMULAE EELATING TO CEANK AND 
PISTON MOTIONS. 



CRANK ANGLE EQUATIONS. 



Upon comparing the positions assumed by a piston under the influence 
of a connecting rod of virtually infinite length, with those resulting from 
the use of a rod of finite length ; it appears that for any point selected in 
the forward stroke (as e. Fig. 53) 

Fig. 53. 




the piston is advanced beyond its normal position by a distance ef equal 
to the ver. sine of the angle a included between the connecting rod and 
centre line of the engine. On the return stroke it will be found in arrear 
by the same distance. 

The object of this investigation is to determine formulas for ascer- 
taining the crank angle due to a certain length of connecting rod and 
position of the piston. 

Let the length of the crank arm A C (in inches) =Tc and that of the con- 
necting rod A B (in inches) = G ; their ratio will be that of k : G ; but if 

— = jg the ratio of the crank arm to the connecting rod will become 1 : N. 



164 CEANK ANGLE EQUATIONS. 

Again the distance of the piston from the commencement of the stroke (in 
inches) = /, consequently : — 



cos A - 



for an advance less than % stroke = — — Z. 

U 1 u i _f ' ~ k 

l—F- 



In which the angle A is a location the crank would assume, if the ratio of 
crank arm to connecting rod were that of 1 : oo . 

Considering <t> as the correct angle for the crank, when the ratio is that 
of 1 : N and its advance less than the first half stroke, we have :— 
Ce = Jc. cos <p. 
/B = G. 
eB = G. cos a 
but, Ce=fB-eB + Cf. 

or Jc cos = G — G cos a + Jc cos A. 

Dividing both members by Jc 

cos (j> = N — N cos a + cos A (1.) 

or, cos $ — cos A = N (1 — cos a). 

cos <t> — cos A 
cos a = 1 (2.) 

Since the " sides of plane triangles are proportional to the sines of their 
opposite angles " it follows : — 

N : 1 : : sin <j> : sin a 

sin 6 

Transforming 

this equation upon the principle that cos 2 a = 1 — sin 'a. We obtain : — 

Substituting this value of cos a in Eq. No. 2 gives 



J I sin>\ cos? — 



cos A 



Squaring both members of the equation ; — 

sin 2 _ . cos (j> — cos A cos 2 <£ — 2 cos <j> cos A 4- cos 2 A 

and multiplying by W : — 

W — sin 2 <£ = N 2 — 2 N cos $ + 2 N cos A + cos V — 2 cos <p. cos A + cos 2 A 
cancelling and changing signs. 



CRANK ANGLE EQUATIONS. 166 

Sin -ci = 2 N cos <p — 2 N cos A — cos 2 <£ + 2 cos 0. cos A — cos 2 A 
or 

(sin 2 9 -f cos '<?>) — 2 N cos $ — 2 cos f cos A = — 2 N cos A — cos *A 
which reduces to : — 

— 1 + 2 N cos (j> + 2 cos <£. cos A = 2 N. cos A + cos 2 A 
or 2 (N + cos A) cos tf> = 2 N cos A + (1 + cos 2 A) 

N cos A + (i cos 2 A + 0.5) 

. • . cos <b = r—^ i (3.) 

r N + cos A l ' 

When the piston stands at the half stroke point, the angle A = 90°. 
But since the cos 90° = 0. the equation (3.) will be so modified as to 
read : — 

0.5 

cos * = ^ . ( 4 -) 

For an advance greater than the half stroke the equation No. 1. will 
read thus : — 

m COS (p = COS A — N + N. COS. a 

which followed through similar transformations to those that developed 
equation No. 3. gives finally : 

N cos A — (A cos 2 A + 0.5) 

cos 9 = =--^ (5.) 

r N— cos A ' 



If instead of the total crank angle or its supplement, the irregularity 
due to the connecting rod is required, the question is reduced to finding 
the difference between cos A and cos <p. 

Subtract cos A from both members of equation No. 3. 

N cos A + a cos 2 A + 0.5) 

COS 6 — COS A = ^r— )* COS A 

N + cos A 



Let E = the irregularity, then : — 
E = 



N cos A + £ cos 2 A + 0.5 — N cos A — cos 2 A 



N + cos A 

Multiplying by § and cancelling : — 

1 — cos 2 A 
E = 



2 (N + cos A) 

_ sin 2 A 

~ 2~(NT cos A) 



and similarly for an advance greater than 90°. 



-p _ sin ' A (7) 

2 (N - cos A) v ' J 



166 CKANK ANGLE EQUATIONS. 

With equations 6 and 7 also the term N being given, the irregularity E 
can be determined for all values of A. The latter may be combined, to 
form a scale, by erecting them as ordinates to a straight line and joining 
their extremites. The curved line so described will be a species of the 
cycloid. 



The equations 3 and 5 can 


be modified by making the original 


values 


of cos A, — 








and J —^ — = e. 




read thus : — 






For cut-off less than 


N.C + (K + 0.5) 

1 stroke, cos rf> = — --* — 

2 ' N + C 


(8) 


" " equal to 


0.5 

i cos </» = — 


(9) 


" u greater than 


* « costf- K *- ( ^ + °- 5) 

* COS - ■ 


(10) 



General formulas for finding that crank angle, which corresponds with a 
given position of the piston. 

It will be observed that equation No. 8 applies to all piston advances 
less than the half stroke in the forward motion, and greater than the 
same in the return motion; while No. 10, on the contrary, solves those 
greater than the half stroke in the forward and less in the return motion. 



EXAMPLES. 

Mo. 1. The stroke of a certain engine = 3£ y . 

The cut-off takes place at 20". 

Ratio of crank arm to connecting rod 1 : 5. 
Required. 

The angles of the crank at the moments of cut-off 



Since the cut-off is greater than the half stroke 
__f~-Jc _ 20 - 16 
e ~ ~¥~ ~ -— 16 ~~ 

For the forward stroke equation No. 10 



= 0.25 



cos , = Xe-J^+J^) 1.25 -(.03125 + 0.5 ) 
Y N - e 5 - 0.25 

And .-. <j> = 81°. 18'. 

Supplement of <j> = 98°. 42' = crank angle forward. 



CEANK ANGLE EQUATIONS. 1G7 

Again, substituting N and e in equation No. 8 gives : — 
5. x 0.25 + (0.03125 + 0.5) n nnnn 

cos ^ = — , — _l___ ; =0-3393 

searching in a table of natural cosines for this decimal, we find that :— 

<p = 70°. 10' and 
supplement of = 109 2 . 50' = crank angle of the return stroke, or the 
second of the two angles sought. 

They have both been given in the Stroke Table column for the ratio 
1 : 5, and line for 0.625 piston position. 



No. 2. Stroke of engine = 10' 6 /; . == 126." 

Cut-off of steam at 33"£. 
Ratio of crank arm to connecting rod = 1 : 7^. 



The angles of the crank at the moment of cut off. 



The cut-off being less than one-half the stroke 

Jc-f 63-33.5 AJ „™ 
C = -¥--=- -63— = (U6826 

This substituted in equation No. 8 gives : — 

A 7.4 x .46826 + (.10965 + .5) AR1Q 
cos * = 7^+168 -' = °.™ 

And from a table of natural cosines : — 

<j> = 58°. 49' = crank angle forward. 

Proceeding in like manner for the return stroke with equation No. 10 

3.46512 - (.10965 + .5) 
PQ8 , = ^-^ 1 = 0.4119. 

^ =. 65°. 40' = crank angle of the return stroke. 



No. 3. What irregularity is impressed on a valve at its half travel 

by a ratio between the eccentric throw and length of eccentric 
rod of 1: 25.? 

5 5 
From Equation No. 4, cos <p = ^=- == ^=- = 0.02 

N 25 

. • . = 88°. 51'. and the 

Irregularity (or complement of <£) = 1°. 9'. about 1°|, which for any given 
travel may be measured from the Base Line of the Travel Scale. 



168 CRANK ANGLE EQUATIONS. 

The irregularity for many other ratios is given below : - 



Irregularity for ratio 


1 


:40 = |° 


Ratio 1 


8 =3°| 


u 


a 


1 


: 30 = |° 


1 


7 = 4°| 


(( 


a 


1 


20 = 1°| 


1 


6 =4°f 


u 


(( 


1 


15 = ir 


1 


.5 = 5°f 


K 


(( 


1 


: 12 = 2°| 


1 


: U = 6°| 


a 


a 


1 


10 = 2£° 


1 


4 = 7i° 



tfo. 



4. When a valve, having an eccentric throw and rod ratio of 
1 : 6 attains its quarter stroke (30°) point, by how many degrees 
does it stand in advance of the position it would occupy were the 
throw and rod ratio that of 1 : oo ? 



Referring to equation No. 7. we observe that in this case A = 60°. 
and as ; cos 60° = £ sin. 60° = \ V3 and sin 2 60° = £ the equation 
for E will become : 

3 



E = 



2N - 1 8N - 4. 
Also , cos <p = cos A — E, or <j> = cos - 1 (.5 — E) 
Since the angular correction = <f — A°, 



we have 



= cos - 1 (5 - E) - 60°. 



By substituting 6 the value of N in equation for E, we obtain :- 
Correction = cos - 1 (5 — .0682) — 60°. 
" = 64°, 25'. — 60° 

" = 4°. 25 ' = amount in advance. 



In a similar manner, we can determine the extent of the irregularity, 
which may be expected from other ratios, at the quarter stroke or 30° 
angular advance point, and measure their linear value from the 30° line on 
the Travel Scale. 



Ratio 1 



30 between eccentric throw and rod, gives ; 



<t 


1 


25 ' 


c « 


a 


1 


20 < 


t u 


u 


1 


15 ' 


( « 


U 


1 


10 ' 


i u 


u 


1 


8 


t « 


a 


1 


7 ' 


c u 


a. 


1 


6 ' 


I u 


a 


1 


5 < 


( u 


U 


1 


4 < 


( « 



1° 

1*° 

lf° 

2|° 
31° 
3f° 
4|° 
5f° 



INDEX 



Adjustable eccentrics, 75. 
Adjustment of link motions, 100. 
Allen Engine, 17, 18, 76. 
Allan Link, 92. 
Ample port opening, 71. 
Analysis of Link motion, 96. 
Analysis of slide valve motion, 31. 
Analysis of Adj ustable eccentric, 76. 
Angular advance, 34, 87, 111. 
Angularity of connecting rods, 56. 
Area of steam port, 21. 
Applications of Link No. 1, 126. 
Applications of Link No. 2, 133. 

Back action engines, table, 57. 

Back pressure, 16. 

Belts, 40. 

Block of link, 93. ' 

Box link, 136. 

Bridge width, 47 

Centre of suspension, 114 

Clearance, 155. 

Connecting rods, 56. 

Connecting rods, short, 121. 

Connection of eccentric rods, 102. 

Constant lead, 78, 80, 82. 

Constant lead and shifting link, 103. 

Corliss engine ports, 23. 

Corliss engine speed, 17. 

Correct crank angles, 63. 

Correct link radius, 102. 

Correction of Exhaust closure, 124. 

Crank and valve motions, 31. 

Crank motion, direction, 39. 

Crossed rods, 102. 

Cut-off, how accomplished, 33. 

Cut-off, equalized, 65. 

Cut-off, independent, 150. 

Direction of crank motion, 39. 
Distribution of the slip, 120. 
Dodds' Wedge motion, 84. 
Driving belts, 40. 

Eccentric, 30. 

Eccentric and valve connection, 61. 

Eccentric for portable engines, 85. 



Eccentric rods, how connected, 101. 
Eccentric rod pins, 125. 
Edges of slide valve, 25. 
Effective pressure from practice, 16. 
Effective steam port area, 23. 
Elliptic solution unnecessary, 44. 
Equalized link motion, 107. 
Equalization of lead opening, 63. 
Equalization of Exhaust closure, 64. 
Equalization of cut-off, 65. 
Exhaust closure, 34. 
Exhaust port width, 48. 
Experiments on area of steam port, 22L 

Flow of liquids and gases, 24. 

Foot-pounds, 11. 

" Force de Cheval," 14. 

Fractions of an inch, 48. 

Friction, 156. 

Friction of engines, 13. 

Gear, full and mid, 77. 

Geometric solution, principles, 106, 109. 

Gooch's link, 92. 

Hanger, 93. 

Horsepower, nominal and indicated, 12. 

Horsepower, actual, 13. 

Howe's Link, 92. 

Inches expressed decimally, 48. 
Independent cut-off, 150. 
Indicator test, 67. 
Inside lap, 35, 48. 
Inside clearance, 35, 48. 
Irregularities of piston motion, 56. 
Irregularities of valve motion, 62. 

Joint action of two eccentrics, 92. 

Kilogramme, 11. 
Kilogrammetres, 11. 

Lap, 33, 114. 
Lap angle, 34. 
Lap circle, 95. 
Lead, defined, 40. 
Lead angle, 42. 



170 



INDEX. 



Lead opening-, 43. 

Lead opening equalized, 63. 

Lead circle, 95. 

Lead, full and mid gear, 118. 

Length of eccentric rod, 62. 

Limit to single eccentric cut-off, 35. 

Limits of lead angle, 43. 

Link motions, 91. 

Link motion, general dimensions, 106. 

Link, box, 136. 

Link, stationary, 92, 137. 

Link, Allan, 92, 140. 

Link, Walschaert, 92, 144. 

Maximum travel of valve, 23, 118. 

Mid-gear travel, 113. 

Mid-gear lead opening, 81. 

Minimum travel, 23. 

Momentum of reciprocating parts, 35. 

Neutral position of valve, 31, 48. 
Number of revolutions of crank, 20. 

Open rods, 101. 
Open link, 128. 
Overtravel, 47. 

Piston motion, 56. 

Piston speed, 17. 

Piston diameter and area, 18. 

Piston stroke, 19. 

Piston valves, 155. 

Portable engine eccentric, 85. 

Port area, steam, 21. 

Ports of the Corliss engine, 23. 

Practical observation on link motion, 

104. 
Pressure, mean effective, 14. 
Pressure, volume and temperature, 15. 
Principles of shifting link motion, 94. 

Qualities, essential and non-essential, 

107. 
Quantity of work, 11. 

Radius of link, 122. 
Ratios of crank to connecting rods, 57. 
Reciprocating parts, 35. 
Reciprocating and link motions, 158. 
Reduction of the slip, 119. 
Regulation of steam admission, 75. 



Revolutions of crank, 19. 
Revolutions of driving wheels, 20. 
Rocker, 31. 
Rocker arms inclined, 105. 

Saddle, 93. 
Shifting link, 92. 
Slide valve, how set, 72. 
Slip of link, 100, 118. 
Slip distributed, 120. 
Slip, how reduced, 119. 
Slotted cross-head motion, 27. 
Speed of piston, 17. 
Stationary link, 137. 
Steam port area, 21. 
Stroke of piston, 19. 
Stroke Table, 58, 59, 60. 
Stud location, 114. 
Suspension point, 101, 130. 

Table A, 28. 

Temperature of steam, 15. 

Template of link, 95. 

Test with indicator, 67. 

Throttle, 76. 

Travel of valve, 23. 

Travel Scale demonstrated, 36. 

Travel in mid gear of link, 113. 

Travel, how diminished, 157. 

Tumbling shaft, 93. 

Tumbling shaft location, 117. 

Unequal lead, 123. 

Unit measure of rods, 56. 

Unit measure of stroke, 26. 

Use of the Travel Scale, 37, 44, 49. 

Valve, 31, 45. 
Valve edge, 25, 45. 
Variable lead, 78, 80. 
Vertical cylinders, 71. 
Volume of steam, 15. 

Walschaert link, 92. 
Wedge eccentric motion, 84. 
Weisbach's experiments, 24. 
Width of bridge, 47. 
Width of exhaust port, 48. 
Work, 11. 

Zero point of stroke, 28. 



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11 The most lucid, accurate, and useful of all the hand-books on this subject that we have yet 
Been. It gives forty-seven tables of comparison between the English and French denominations 
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instructions how to use them ; and to this practical portion, which helps to make the transition 
□s easy as possible, is prefixed a scientific explanation of the errors in the metric system, and 
how they may be corrected in the laboratory." — Nation. 

BAUERMAN. Treatise on the Metallurgy of Iron, containing 
outlines of the History of Iron manufacture, methods of Assay, 
and analysis of Iron Ores, processes of manufacture of iron and 
Steel, etc., etc. By H. Bauerman. First American edition. Re- 
vised and enlarged, with an appendix on the Martin Process for 
making Steel, from the report of Abram S. Hewitt. Illustrated 
with numerous wood engravings. 12 mo. Cloth. $2.50. 

'* This is an important addition to the stock of technical works published in this country. It 
embodies the latest facts, discoveries, and processes connected with the manufacture of iron 
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technical and scientific libraries."— Scientific American. 

HARRISON. Mechanic's Tool Book, with practical rules and sug- 
gestions, for the use of Machinists, Iron Workers, and others. 
By W. B. Harrison, associate editor of the "American Artisan." 
Illustrated with 44 engravings. i2mo. Cloth. $2.50. 

41 This work is specially adapted to meet the wants of Machinists and workers Id iron gener- 
ally. It is made up of the work-day experience of an intellfgent and ingenious mechanic, who 
had the faculty of adapting tools to various purposes. The practicability of his pluns a»4 sug- 
gestions are made apparent even to the unpractised eye by a series of well-executed wood t>o 
pavings."— Philadelphia Inquirer. 



28 D. Van Nbstrand's Publications. 

PLYMPTON. The Blow-Pipe : A System of Instruction in its prac- 
tical use, being a graduated course of Analysis for the use of 
students, and all those engaged in the Examination of Metallic 
Combinations. Second edition, with an appendix and a copious 
index. By George W. Plympton, of the Polytechnic Institute, 
Brooklyn. i2mo. Cloth. $2. 

" This manual probably has no superior in the English language as a text-book for beginners, 
or as a guide to the student working without a teacher. To the latter many illustrations of the 
utensils and apparatus required in using the blow-pipe, as well as the fully illustrated descrip- 
tion of the blow-pipe flame, will be especially serviceable." — New York Teacher. 

NUGENT. Treatise on Optics : or, Light and Sight, theoretically 
and practically treated ; with the application to Fine Art and In- 
dustrial Pursuits. By E. Nugent. With one hundred and three 
illustrations. i2mo. Cloth. $2. 

" This book is of a practical rather than a theoretical kind, and is designed to afford accurate 
and complete information to all interested in applications of the science."— Bound Table. 

SILVERSMITH (Julius). A Practical Hand-Book for Miners, Met- 
allurgists, and Assayers, comprising the most recent improvements 
in the disintegration, amalgamation, smelting, and parting of the 
Precious Ores, with a Comprehensive Digest of the Mining Laws. 
Greatly augmented, revised, and corrected. By Julius Silversmith. 
Fourth edition. Profusely illustrated. 1 vol., 12 mo. Cloth. $3. 

C LOUGH. The Contractors' Manual and Builders' Price-Book. By 
A. B. Clough, Architect. 1 vol., i8mo. Cloth. 75 cents. 



B 
C 



RUNNOW. Spherical Astronomy. By F. Brunnow, Ph. Dr. 
Translated by the Author from the Second German edition. 1 
vol., 8vo. Cloth. $6.50. 

HAUVENET (Prof. Wm.) New method of Correcting Lunar Dis- 
tances, and Improved Method of Finding the Error and Rate of a 
Chronometer, by equal altitudes. By Wm. Chauvenet, LL.D. i 
vol., 8vo. Cloth. $2. 



A 



SYNOPSIS OF BRITISH GAS LIGHTING, comprising the 
essence of the " London Journal of Gas Lighting" from 1849 to 
1868. Arranged and executed by James R. Smedberg, C. E. of the 
San Francisco Gas Works. Issued only to subscribers. 4to. Cloth. 
$15.00 In press. 

GAS WORKS OF LONDON. By Zerah Colburn. i2mo. Boards. 
60 cents. 

HEWSON. Principles and Practice of Embanking Lands from 
River Floods, as applied to the Levees of the Mississippi. By 
William Hewson, Civil Engineer. 1 vol., 8vo. Cloth. $2. 

" This is a valuable treatise on the principles and practice of embanking lands from river 
loods, as applied to Levees of the Mississippi, by a highly intelligent and experienced engineer. 
The author says it is a first attempt to reduce to order and to rule the design, execution, and 
measurement of the Levees of the Mississippi. It is a most ueelid and need»»v. contribution Ut 
■ ientific literature."— Ph iladelphia Evening Journal. 



